IM 8.5.20 Lesson: The Volume of a Sphere

Here is a method for quickly sketching a sphere:
[list][*]Draw a circle.[/*][*]Draw an oval in the middle whose edges touch the sphere.[/*][/list][img]data:image/png;base64,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[/img]
Practice sketching some spheres. Sketch a few different sizes. For each sketch, draw a radius and label it r.
[size=150]Here are a cone, a sphere, and a cylinder that all have the same radii and heights. The radius of the cylinder is 5 units. When necessary, express all answers to the following questions in terms of [math]\pi[/math].[/size][br][img]data:image/png;base64,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[/img][br][br]What is the height of the cylinder?
What is the volume of the cylinder?
What is the volume of the cone?
What is the volume of the sphere? Explain your reasoning.
[size=150]Here are a cone, a sphere, and a cylinder that all have the same radii and heights. Let the radius of the cylinder be [math]r[/math] units. When necessary, express answers in terms of [math]\pi[/math].[/size][br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAfoAAADHCAYAAADxhpGOAAAgAElEQVR4nOydd3hURduHZ1OAEAihQyAUkd5BJIC0AFKkRGmiLwakKYpKR1CUZmyIoAIKSkep0lRaEBAi0oIQekILJQFCIKRvkvv7I985nt3spiwpW+a+rnNBTts5037zzDwzI/h/0tLSkEgkEolEYl8I5T9S6CUSiUQisT+k0EskEolEYsdIoZdIJBKJxI6RQi+RSCQSiR0jhV4ikUgkEjtGCr1EIpFIJHaMFHqJRCKRSOwYKfQSiUQikdgxUuglEolEIrFjpNBLJBKJxCLS0tJITU0lJSUFvV6PXq8nJSWF1NTUgg7aE6F8l/ablO+yRa2UQi+RSCQSk2iFXCt2OSEmJobbt28TGhrKyZMn+fPPP9mwYQNLlixh3rx5TJ8+nffff58333yT119/nZdeeonevXvTsWNH2rVrR/v27Wnbti0NGjSgfv36Jo9mzZrRvn172rdvT7t27ejatSu9e/fm5ZdfZvjw4bz77rtMmzaN2bNn8+2337J8+XK2b99OUFAQZ86c4fr169y9e5fExMQcfZtxvFirjkqhl0gkEomBZZ4dMY+Pj+fq1ascOnSIn3/+mYCAAN5991369etHq1atqF27NqVKlcLV1RUhRIbDzc2NMmXKULZsWapVq0bt2rVp2rQprVq14vnnn8fPz4/evXvz6quv4u/vz5AhQzI9/P396d+/P71796ZPnz60b98eHx8fGjRoQK1atfDy8qJcuXJ4enri4uJiMkxFixalYsWKNGrUiE6dOjF48GCmTJnCggUL2L59OydPniQyMhK9Xp9p3KSlpRnEZUHrqxR6iUQicTAUIUpJScm07n/48CEhISFs3ryZTz75hJdffplWrVpRuXJlihQpogqkk5MTpUqVombNmrRs2RI/Pz9Gjx7NzJkzWb58OVu3buXgwYMEBwcTFhZGVFQU8fHxBdLFn5ycTExMDHfu3OH8+fMcPXqUvXv3snHjRhYuXMjUqVMZMmQIXbt2pXHjxlSpUgV3d3eDBkGJEiWoVasWnTp14o033mDRokXs3buXa9euZdoroDSm8lv8pdBLJBKJnaMVdlMkJydz6dIlNm3axNSpU+nSpQtVq1Y1sMZLly5N06ZN6d+/P5MnT2bx4sXs2rWLkJAQ7t+/nyvhNB4myI0jN7QtKSmJ8PBwjh8/zqZNm/jiiy8YPXo0Xbt2pWbNmhQtWlSNp+LFi1OvXj0GDRrEl19+yZ9//snt27dNvldJl7wWfin0EolEYocoommKmzdvsmXLFt577z1atGiBh4eHKlQVK1akU6dOjB8/nh9//JGgoCBu3ryZbY3QNiqMx7AVQStovVHCoITJXAMju+GMi4vj8uXL/PHHH8ybN4+hQ4fStGlTg56ASpUq0aNHDz799FOCgoKIiYnJ8B4lHLkdP1LoJRKJxE4wJ+43btxg5cqVDBo0iKpVq6ri4+3tTd++ffniiy/Ys2ePWctTQTv2bAtOaLmJsWNidsbfExISuHDhAhs2bGDixIm0bdtWbVQVLlyYZs2aMX78ePbs2UNsbGyG38st0ZdCL5FIJDaMIgha9Ho9gYGBjBkzhtq1ayOEQKfT0aRJE9555x02btzItWvXzL5TK2iOIuRPgtJDkJ3egOTkZIKDg1m4cCEDBgygUqVKqiNgx44dmTdvHpcvX87wfnO9M9lBCr1EIpHYIEqXs0JKSgr79u1j+PDhlC5dGiEEXl5e+Pv7s379eiIjI02+J7fHsyWGGDeaTBESEsK8efPo0qWL2t3ftGlTPv/88wyib0k6SaGXSCQSG8LYwg4LC2Pq1KlUqFABIQQ1atRgypQpnDhxIsOz2fW2l+QtWvE3JjY2lm3btjFgwACKFSuGEILmzZuzcuVKEhIS1PtykoZS6CUSicQGUMaIFfbv30/37t0RQuDu7s6YMWM4depUhueksFs/2ml3WmJjY9m8eTOdOnVCCIGnpyfjx4/n5s2b6j3Z6dKXQi+RSCRWjlYAgoKC6NKlC0IIGjduzLJly3j8+LHB/fawDK2jYm4q5OXLlxk/fjzFihXDycmJyZMnc+/ePfWZzDRcCr1EIpFYMUqFHx0dzeDBgxFC0LBhQ7Zs2ZLhPinu9oV2nr3Co0eP+PjjjylatChubm4sXbrU4H5TSKGXSCQSK0UR+V27dlGhQgU8PDxYvXp1hntk/W3/GHve379/nzfffBMhBH369FGdLU019qTQSyQSiRWiVNgrV65ECEGvXr2IiIjIcF3iWBgL/u7duyldujRVq1YlPDxcvUeLFHqJRCKxMpT6+Oeff0YIwcSJE9VrTzKfWmI/aAU/MjKSunXrUq1aNSIjIzOM2Uuhz0esYelHiURi3Sh1RHh4ODqdjtGjRwMZp9VJJIC6k15UVBRlypShR48egGGPjxR6icTGMbVneE7GbU2tTS5FpeBQ4r1v3754eXmRlJQk00OSKVpfDiEEe/bsMbguhT4fUOI2LCxM9ZSV8S3JKYqgK+uM5yQPJSQkEBcXpx4JCQk5bghYy97ajkBMTAyurq7Mnz8fkN31kqxRLHhl5zwtUujzAaWQjhs3jrJly5KcnCzjW5ItzC2koaDX67l16xYHDx5kyZIlvPPOO/Tr14+OHTvSpEkTqlevTvny5XFzc8PFxQVXV1dcXFwoUqQIZcuWpUqVKjRs2JD27dvj5+fHqFGj+Pbbb9mzZ0+me2vn1/aajoaSzqdPn0YIwZEjRwBZP0uyRimPw4YNo0GDBgbXpNDnMUq83rt3T11/+qeffgJkK12SEVPzZhXi4+M5ePAgc+bMYeDAgTRt2pSSJUuqO5EVLlyY6tWr07p1a3r06IG/vz/jxo3jk08+YeHChSxevNjg+Pzzz5kwYQKvv/46PXv2pG3bttSqVcvk3tp+fn58+OGH7N69m+jo6Axhy6vtNR0NJd3PnDmDTqdjx44dBuclEnMoeaRbt25S6PMbJfInTpxI4cKFqVevHtWrV5dWvcQAU9uLJicnc+zYMQICAujQoYO62YWHhwctWrTglVde4dNPP2Xr1q1cuHDB5P7WlhAfH09YWBg7d+5k3rx5DBs2jDZt2lC2bFmEELi6uvLss88ybdo09u/fn2F7TSn6lqPEWUhICDqdjgEDBgDSKJBkjuLofefOHdzd3fHx8TG4LoU+D1HiNCoqisKFCzN27FiCg4MRQvDjjz8CsqXuyJgS90ePHrFy5Uq6d+9OiRIlVGHv1KkTX375JSdOnCApKSnL9yrv1u4bbupQrivPZFYPpKWlcf78eb777jv8/PwoV66cur3mc889x4IFCzLsZy5Xa8sZxl33Qgh+//134D/vaolES1pampo3Xn31VYQQdOjQweAeKfR5iFJo33//fYQQXL9+HYBnn32WypUrS6veQTEW1JSUFHbt2sWgQYPUbvM2bdowZ84c/vnnH5PCbizkuTlWbmpvbVNinZaWxunTp5k/fz5du3bFxcUFJycnunfvzqZNm4iPjze4X1qlWaPEc3BwMC4uLtSuXZsiRYrwzz//AHIVPIkh2nI5bdo0hBB4e3tLiz6/iYqKokiRIgwbNgxIj+f9+/cbWPWyAnQMjMX4zJkzTJgwQd1etFatWgQEBKgNQuNnrcE6zmx7zfv37/PDDz/QokULdUe1oUOHcvjwYYP7ZH43j5K+//77L05OThw5coSXX34ZZ2dntm/frt4n49Cx0S6Wk5yczJgxYxBCsHnzZt5++23q1q1rcL8U+jxCSYT3338fnU6nLk2oFGQfHx9p1TsIxpXy/v376dChA0IIypUrxzvvvMOxY8cM7rEWYc8Kc+E8f/4806ZNo3r16gghaNKkCRs2bDC4R4pVRoy77o8fPw781yU7bNgwg53qpIXvWBgvf3v06FHq1KmDk5OTugeCv78/9evXN3hOCn0eoB2bd3NzU615ZRwUkFa9A2Asfjt37sTHxwchBM2aNWPjxo0kJycb3GPLFbdSCRmHPzAwEF9fX4QQ1KlTh1WrVhnEjbU3ZvITrUWv0+kICgpSr61evRp3d3dKlSrFggULDMbsbaFRKLEc497AsLAwhgwZghCC1q1bc/HiRfW+IUOGSK/7/EApcFOmTEEIwY0bNwyWv1X+9fHxwdvbW1r1doZxq3vLli00btxYLZQ7d+40uN8eK2lTjoZHjx7lhRdeQAhBtWrVWLJkidrQkfPx09EKvXYevSLqN2/eZMSIEepY7OLFi3n06JHBO2y5sSj5D1Nl6OLFi+qOdeXKlWPRokXqNcWXZ+jQodKiz2u01rx2bF6bYNKqt1+0afjXX3/RrFkzhBB06tSJwMBAs/faM9qeLEgXsX79+iGEoHLlymzevFm95ihxYg5jof/777/V89q4uXDhAoMGDVJ9Id566y1Onz5t8K7M1mSQWB9aB1gtKSkpbNmyhY4dOyKEoEyZMnz55ZckJCQYPKuk85AhQ6TQ5zWmrHnIGL/KfS1btpRj9XaAtjK9e/cuw4cPRwhBq1atOHTokHpNWyAdDWPBv3jxIi+99BJCCLp3787ly5cN7nVEMhN6yNhbdO3aNaZPn0758uURQtCgQQM++eQTtStXS2YzKCT5j3aPCuO6Pzk5mcDAQIYPH66uX9GyZUtWr15tsFqlNi8o/5dCn8co3fOKNf/6668Dpistc1a9LIS2h7awLV26FA8PDzw8PFi6dKl63ljkHBnjuPjtt99Up70ZM2aoXZCOGF9ZCb2CcYMxOTmZTZs24efnh5ubG0IIGjduzMyZMzl69KjJnhKtI6Ws//MercVuKr7v3bvHli1b8Pf3V1e8rFy5srr+ihZT6SmFPp8w9rQ3Z80raMfqpVVve2j9Lk6ePKk62o0YMYJ79+6p9zmiYGUHrVglJyfz0UcfIYSgevXq/PHHH+p9jhR/2RV6BWMLH+Dx48ds2rSJvn37qoJRqlQp+vTpww8//MC5c+fMDpFoN01ypHjPTYx3kzQXj48ePeLQoUPMnDmTFi1a4OTkhBCCGjVqMHbsWNU/Q/vezIa2pNDnA+bG5jMrLHKs3nbRpuuXX36JEIKmTZsazBmX6Zg9tPF06dIlunfvjhCCd999V41nR4nLnAq9FlOiotfrOXLkCB999BHPPPMMLi4uqvB37tyZ2bNnc+DAAe7evZvlu+UWxv9hLObKzo7m0Ov1hIWFsXHjRt5++20aN25M4cKFEUJQsmRJevXqxffff09oaGiGZ7Pb6JJCnw8okayMzYeHhxtYfOaQVr3toaT1gwcPePHFFxFC8PHHHxtcl2mYc7RivmzZMnQ6Hc2aNSMsLCzDdXvlSYRewZxTF6QbIoGBgXz88cf4+vri6empLrVbpUoVunfvzkcffcSOHTu4ePFihtUNzYXZeGll7ZLKtlQWlPCa+qbs5r/79+8THBzMsmXLeOutt2jZsqXB5lPVqlVj0KBBLFq0iNOnT5tc2tiSHhUp9PnEgwcPcHNzy3Rs3hhp1dsWSnoFBQXh5eVFyZIl2bNnT4brEsvQdueHhIRQr149ChUqZLDYjj3XVbkh9Kbeaa7xmZyczLlz51izZg3jx4+nffv2qvOXso9BzZo16dGjB+PHj2f58uUcPHiQsLAw4uLiLAqLsSVsbj8G5V5LD1P7Omh/Lzv7O5j7hqioKEJCQti1axdff/01w4cPp02bNnh5eeHs7IwQAhcXF55++mlefPFFAgIC2LlzJ7du3cpxGmUXKfR5jPGa9lmNzRsjrXrrR5sec+fORQhB586diYiIAGTDLLdR4jMhIYFhw4apXfmK9WOvDaq8EHotSkMqs67mtLQ0wsPDCQwMZOHChbzxxhv4+vri7e2Nq6ur2ggoUqQIlSpVokWLFvTr149x48Yxb948fvnlF/bt28fZs2eJiIiwqEFQEOj1eh4+fEh4eDjHjh3j999/Z9myZcyZM4c33niD7t27U69ePcqUKaOOpwshKFasGHXr1qVPnz5MmTKFNWvWcPToUZPbOSvkxQwIKfR5jOJpb7wKXnaRHvjWjZIOer2eV155RfUOV5Ainzdo8/+KFSsQQuDj48P9+/czXLcX8lrozf1mdoUnOjqa8+fPExgYyJIlS5g6dSoDBw7Ex8eHqlWr4uHhYdAYUOb5lylThqeeeopGjRrh6+tLnz59GDp0KJMmTWL69Ol89dVXfPvttyxfvpw1a9bw+++/s2vXLg4ePMiJEyc4efIkwcHBmR4nT57k+PHj7N27l927d/Prr7+yatUqli5dyjfffMOnn37KBx98wLvvvsugQYPo0aMHrVu3pm7dunh7e+Pp6amOmytH4cKFKVOmDLVr18bX15fhw4fzySef8Msvv3DkyBGuXbuW5W6S2l6FvNRZKfR5iNaaz46nvTmkVW+dKOkbExNDhw4dcHZ2Nuiql2mU9ygV2OnTp/Hy8uKpp57i6tWrBtfshYIQelNk13PcmOTkZKKiorhy5Qp///03W7ZsYfHixXzyySeMHTsWf39//Pz8aNu2LQ0bNqRatWqUKVOGcuXKUbx4cdzd3Q2E9kkOnU6Hk5MTxYsXx8PDg3LlylG+fHlq1qxJ8+bN6dy5M/3792fEiBG8//77zJ07lxUrVvDHH3/w77//Eh4enmHVwcwoaIdFKfR5hBJnDx48yHLefFbIsXrrQ4n7O3fu0KBBA0qUKMHJkycBuTd4fqPE9+3bt6lbty6lSpXi1KlTgH2VEWsRenMoDQClEZBbU/FSU1NJTEwkNjaWqKgoIiIiuHz5snoEBwfzzz//cPToUZPHP//8w9mzZwkNDeXy5ctcuXKFqKgooqOjSUhIICkp6Yk0zpSDnrXNPpBCn0eY8rQHy+NSroFvPShpGxoaSuXKlalatapDeX9bI4qYPHz4kLZt2+Lq6sr+/fsB+0kTaxf67GDKc93Y4a6gRdKcs55x+Gyp/pVCn4dY4mlvDmnVWwdKOhw7dgwPDw+aNm2qzjOWaVGwaBfYUZbP3bRpE2AfaWMPQv8kKOJqfGTX097Us46CFPo8wNTYfG5kLDlWX7AoheXEiRO4urri6+ureg07SmVr7WjLg7KnwMaNGwHbF3tHF3qJ5Uihz2UsWQUvu0gP/IJDiePQ0FCKFStGx44d1XMy/q0LbaN65MiRCCHsohtfCr3EUqTQ5zK55WlvDmnV5z9K/EZGRlKpUiWaNm0qLXkrR7u4Tr9+/XB2dlY3/7DVNJNCL7EUKfS5iGJJKJ72uWnNK0irPn9R8n5sbCwNGzakatWq6lxtWS6sG6U86vV62rZtS4kSJbhy5Qpgm+VFCr3EUqTQ5yJaT3udTvfEnvbmkFZ9/qGsFNa+fXubFwpHRCkXjx8/pn79+lStWlXdPdDWyowUeomlSKHPZZRV8HLD094c0gM/f1DieeDAgXbR9euoKOkVERFBpUqVaNasGUlJSTaXjlLoJZYihT6XMLWmfV5O4VDe27JlSzmvPg9QCoayzWxgYKDBeYltoZTPixcvotPpGDFiBGBb6SmFXmIpUuhzAWNPe8Waz8tKxNiq/+mnnwzOSyxHicMjR44ghGDWrFmAbYmCJCNK+q1btw4hBGvWrAFsp8xIoZdYihT6XMDYmr9+/TqQ9/Emx+pzH6UX5vHjx1SsWBFfX19Airy9oKTj6NGjEUJw8eJFwDbqOCn0EkuRQv+E5IenvTmkVZ/7KAXixRdfpHjx4upWs7IM2A+Kg2WDBg2oV68eycnJNlFmpNBLLEUK/ROiFDLF0z63581nhbFVr9frZXpZiJKW8+fPRwjB7t27Dc5L7AOlfISFheHs7Mzw4cMB609nKfQSS5FC/wRox+bz2tPeHNIDP3dQ0vLs2bMIIfjwww8BGY/2ivF4/bZt2wDrFk0p9BJLkUL/BOS3p705pAf+k6OkZcuWLdWCICtQ+0ap/F566SXKli1LfHx8ge+clhlS6CWWIoXeQsx52hdEoZNj9U+GEk/Lli1DCME///xjcF5inyiN8oiICFxcXBg/fjxgvb04UuglliKF3kJMWfNQcHGlteqlB37OSEtLIzo6Gg8PD4YMGQLIytNRUNL5q6++QgjB+fPnDc5bE1LoJZYihf4JyM395p8Uc1a9tVon1oISbyNGjMDd3Z3o6GiH26va0VG66+vWrUurVq3Uc9aGFHqJpUihtwAl0pQd6vJqTfucIufV5wylgjx69ChCCJYuXWpwXuIYKOl9+PBhhBCsXr3a4Ly1IIVeYilS6HOIEhfWZM0rSKs+ZyiWe+PGjWnevDlgHekoyX+UdB88eDCenp48fvzY6uo9KfQSS5FCn0O08+atYWzeGK1VLz3wzaOk4++//44QgmPHjhmclzgWSqPv7t27ODs7ExAQAFhXfpBCL7EUKfQ5wJo87c0h59VnDyUtmzVrRps2bQDrSkdJ/qOk/8iRIylVqhQJCQlWVfdJoZdYihT6HGBtnvbmkB74mWPcGDp48KDBeYljopSR8PBwhBAsWLAAsJ58IYVeYilS6LOJ0rVnzda8gjmr3hrDWhAo+blNmzY0adLE4JzEsVHKyKuvvkqFChVISkoq4BD9hxR6iaVIoc8mWmu+INa0zynSA980Sjr+/fffcj17SQaUMnL58mWEECxZsgSwjqEvKfQSS5FCnw2sYU37nCI98E2jpKWvry9169Y1OCeRwH9lp2/fvlSpUgW9Xl/AIUpHCr3EUqTQZwNrWdM+p0gPfEOUb79w4QJCCDZt2gTIilJiiJJPQkJCrGrDGyn0EkuRQp8F1jxvPiukB74hyndPnjwZT09PkpOTCzhEEmtFKfdNmjShW7duBucKCin0EkuRQp8FtuJpbw45Vm9IamoqFStWZNSoUYDjNnokmaPki0WLFuHs7My9e/cKOERS6CWWI4U+CxRPe1uz5hXkznbpKN978OBBhBAcP37c4LxEYor79+/j7OzMwoULgYJtGEqhl1iKFPpMsDVPe3NIq95w2lT16tULODQSW0DJM926dbOKaZhS6CWWIoXeDNqxeWufN58V0qpPJzY2lqJFizJr1ixAdttLMkcpH1u3bkUIwaVLl4CCqw+l0EssRQq9GbQ71AkhrGaHOktxZA98JS1//vlnhBBcv34dsN20lOQviYmJeHp6MmXKFKDgGohS6CWWIoU+E2zR094cjuyBr3x7jx49eOaZZwDHzdOSnKGUj9dff73Ah3yk0EssRQq9CYw97a9fv24T8+azwpHH6vV6PZ6ennz88ceAfTVwtGmYlpZmUPGnpKSo11NTUw2+W3ufcf7WXktNTTW4ZvwO49+3J5R42Lx5M05OTty6dQsomO+UQi+xFCn0RhjvUDds2DDAPgqT8g1//vmnw4zVK+l56tQphBAEBQUBtvHNmYmtrWHckLC1htadO3fQ6XSsXbsWKJj8I4VeYilS6I2wF097cziaVa9k8C+//JKiRYsSHx9fwCEiVwRP+47Q0FB1nvfVq1fZsmWLem3x4sVcvHgRgN9//52vv/4agKSkJEaMGKE6mC1cuJC5c+cCEBkZyahRo3jw4AEAc+fO5eeffwbgxo0bzJs3T33/5s2bOXfunPpccHCwei0uLs4iETLuabAW6taty2uvvQZIoZfYFlLoNShWhz142pvD0Tzwle/q0qUL7du3B/I/P2u7zzNDr9erq/UlJSXx22+/8fjxYwC++eYb1qxZA8C5c+fo3r07iYmJAAwdOlRdznfPnj1qLxTABx98oIpvUFAQK1euVH9r+fLlREREAHD48GEOHDgAQHR0NMuWLSMuLg6ADRs2EBgYCMC1a9fUWQsA48ePZ8eOHQDs2rVLFUKAF154gb/++guAdevWMW3aNAASEhL44YcfePjwIZDee6b8PysKohGgVJJjxozB29s7X37TFFLoJZYihV6DvXnam8PRrPrExESKFStGQEAAkDfdxtn14UhMTFSt77S0ND755BPVqv7mm294++23gXTxGzhwIHfu3AHSp3gpYvv48WNOnz6t/p5er7fK9Ltx4waxsbFAeuNk7969QHr4R44cqY53T506VfWduHLlCmPGjFEbPGfOnFEbI5mRmpqaZ4KnvHfHjh0IIbhy5QqQ//WCFHqJpUihN8KePO3N4Sg72ynfeeTIEYQQHDt2DMi9/Jzd+Prhhx/Yt28fkG71+vn5qeGYMWMGoaGhAERERHDt2rUnDpe5sX1Tjnra+zK7ll1nPEt4/Pix2nNx7949fvzxR1Xo/f39WbduHZDuWzJ27Fj1W65fv252v/i8KLcPHjzA1dWVZcuWAflfXqTQSyxFCv3/Y6s71FmK8l0tW7a023n1Sub+4osvKF68eK5sYmOucr927RohISEA3Lp1i27duqlj3PPnz1et2fj4+Gyvm27sBW9r3u1ZzQbI6XsuXrzI+vXrgfRejM6dO3P69Gkg3dr+7bffciPYmYahYcOGvPrqq4AUeontIIWejJ72ijVvbxauFkcYq1fS77XXXqNx48ZAzvNyZo29H3/8kfPnzwPpzmwTJ04E0segT5w4ka19zLXj9/bcsMwJ2S13MTExauNt+fLlLF26FICzZ88yfPhwg3jNrTC9+uqrNGvW7InfZwlS6CWWIoUe0/Pmwf6/W2vV2+NYvfItzzzzDAMGDACyJyLmnOdu3LjBpEmTVAGfPHkyJ06cyPJ9tmiNWyPGvQLmiIiIYO3atWo8+/n5cejQISC9RyUhISHHv63kmzlz5lCqVKkCMQKk0EssxeGF3tjT3p7mzWeFI1j1aWlplClTJsv17c198/r16/n8888BuHnzJl988UW2LHV7ikNbIDNfgeDgYO7fvw/A7NmzmTx5MpAxL2SWZsq1LVu2oNPpVCfJ/KwbpdBLLMXhhd7e581nhbEHvrV6cOcU5RuUhU42btwIZK9S/Prrrzl48CAABw4cUJ81xtYXsbFnzKXzvXv3VJE+dOgQvXr1Mnmv8TklnUNCQhBCcPjw4Ux/Jy+QQi+xFIcXenAMT17J2IIAACAASURBVHtz2KsHvvJd//zzD0IIzpw5A2R0EIP0b/3zzz/Vudzz589X538bY+vx4oiYq78ePXrEqVOngPTx/qFDh3L37t1M3/X48WMKFy5cIOVECr3EUhxa6B3N094c9uiBr6Tt8uXLcXFx4dGjR4DpvJycnEzv3r3VFd60ZHdcWGLbxMfHs2TJEnWa34EDB9RZE8ZiXqVKFcaNG2fyWl4ihV5iKQ4r9OY87R2x0NjjWL2SsSdNmkSVKlUyXH/w4AF9+/bl9u3bGa7JLnnHwVQ6p6Sk0KtXL3XdBQWlPHTq1Ilu3boZnMsPpNBLLMVhhd5RPe3NYW8e+ErGHjRoEC1atFDPK450SUlJrFu3jpiYmAIJn8T6MGWdp6amMnPmTK5du6YuKuTv72/xdM0nQQq9xFIcVujBscfmjbE3q14J9/PPP0+nTp1ITU0lISGBLl26qAvbSCRZodfrmTZtGlevXlXPjR8/nmrVquV7WKTQSyzFIYVeu6a9I3ram8OePPCVcLdo0UKdMpmSkkJwcLC6g510rJPkhNDQULZv384XX3xB6dKl811gpdBLLMXhhF47Ni+teUPs0QP/2WefpU6dOixfvryggyKxUZThnkOHDjF27Fh+/PFHihUrlu9bHkuhl1iKwwm9KU97sK9vfBLszQO/Ro0adOjQQd0YxZYbLRLrYPPmzTg5Oale+fmFFHqJpTiU0EtrPmvsaaxer9dTrFgxdQ10KfKSJyElJYXU1FQ2b96MEEIdt8+v+lEKvcRSHEropad99rAXD3y9Xo+HhwfLli3L0/3KJY6Bkn82bdqETqfj4sWLBufz6/el0EtyikMJfVpamrTms4G9WPVxcXG4ubmp+4fbWvgl1oWSf/bu3YtOpzO52mJ+/L4UeklOcRihd/Q17XOKsQe+LVr18fHxFC1alAkTJgCy617yZCj5Z8mSJQgh1JUUpUUvsXYcQuiV8Mt589nHHjzwk5KSqFChAlWqVCE+Pl6mt+SJUPK+r68vOp2OsLAwQFr0EuvHIYRermlvGbbugZ+amkr9+vURQjB16lSAbG0xK5EYk5ycDMDq1asRQuDh4UFkZGS+hkEKvcRS7F7ozVnztmSZFhT2YNU/++yzlC9fHiEE33//PSDXspdkn7S0NDW///HHH7i4uODl5UXlypXVjZLyCyn0Ekuxe6GXnvZPhq164CthbN68OcOHD2fevHkIIZg3b556jy01WCT5jzZ/rFu3DiEEb7zxBl9++SWlSpXK9/wjhV5iKXYv9NLT/slQ4urPP/+0KQ98UzuNzZo1CyEEXbt2VRt8IAVfYog2P8TExDBs2DCEEPj7+wMwdepUvL298z1cUugllmLXQi897XMHrQe+rYzVKxl74MCBtGzZ0qDB4u3tTeHChQkICCA2NtbgGWv/LkneoO2iV/5esWIFFSpUoGjRoqxdu1a9NmTIEBo2bKjel19IoZdYit0KvXZs3tH3m39SbHFevZKxx40bR/Xq1Q3OPX78mLFjxyKEoEyZMsyfP99g3fLU1FQp+g6CstqdQlpaGuvWraNGjRoIIejfvz+3bt0C/nPI69atG76+voDcj15iG9it0Gt3qJNr2j85tuaBr53zXKhQIdVy11pt165dY/jw4aoX9dixY9XVzhSk6NsXiuVuPFxz584d5syZg5eXF0IIevbsyalTp9Tr2vufeuop3nrrrQzn8xop9BJLsVuhBzlvPjexNQ98JbyHDh0yWNxEycvacIeFhTFhwgRKlSqFEIIOHTqwYsUK7t69a/BORSRkPrItlMaacbrFxcWxadMmevXqhRACNzc3hg4dyokTJwye1dZ/8fHxuLm5qTM4pNBLbAG7FHq5Q13eYEtj9Uq4wsPDEUKwbds2gAzdtNqKOjExkdWrV9OmTRuEEDg7O/P888+zcuVKIiIiMvyGVkCsNR4cjbS0NLPCDvDw4UN27NjBoEGD8PDwQAhBgwYNWLBgAVFRUep9xnsjKOl74cIFhBAcOHBAvS+/kEIvsRS7E3q5Q13eYYse+KmpqXh6ehIQEACYtsCMBR/g5s2bLFq0iLZt26LT6dDpdDRr1oz333+fv/76i4SEBJO/p3QLS/HPe7Sibm54JSUlhRMnTvDpp5/Stm1bChUqhBCCRo0aERAQwKVLlzLcbyo/K+d27NiBEILw8HA1DPmFFHqJpdid0EtP+7zFlqx6hSZNmjB48GAg665WU4Jx584dVq5cSf/+/SlTpgxCCIoXL0779u35+OOP2bdvn4E1aOqder1eNgAsRCvoSjyaIyYmhqCgID777DN69OhB6dKl1fTq0aMHCxcuJDQ0NMNzWflhKPXK559/joeHB0lJSU/+YTlECr3EUuxK6KWnfd5jSx74SpgGDhzIM888A2Q/L5sbj09JSeH48eN88sknPP/886rwOzs7U69ePfz9/Vm4cCFBQUE8ePAgy/CZagTYSnnLTYytc71en2WeiomJ4eTJkyxbtow33niD5s2bU7hwYYQQFCtWjOeee44PPviAgwcPmuyByYm/hbaibNSoUc4/MBeQQi+xFLsSeulpnz8Y72yn1+utMo6V/DBr1ixKlixpseOUOU9t5VpISAjLli3D39+fevXq4ebmpop/jRo16NWrF9OnT2ft2rWcPHmSe/fu5fh3tYcyfmzNjQIlbEpYTX1HdsMeHR1NSEgImzZtYs6cOfTr14/atWur3fCurq48/fTT9OvXj2+//ZaTJ0+SmJiY4T1PMoNCeaZZs2b0798fyH9HVCn0EkuxK6EH6WmfH9iKB74SzgMHDiCE4OzZs8CT5+fMnL0AYmNj+ffff1m+fDljxoyhdevWVKhQAScnJ4QQODk5UaFCBVq3bs2QIUOYMWMGq1at4tChQ4SGhhIXF2dx2IwtY1OHXq/P8ZHZ+550OCIhIYFr165x5MgR1q1bR0BAACNGjKBDhw54e3vj6uqKEEJd9+CZZ55h5MiRLFq0iKNHj5rtOckqnXLKo0ePKFSoEN9++y0ghV5iO9iN0Msd6vIX43n11mrVQ/o0qiJFijB//nwg9yvorBzCFO7fv8/x48dZu3YtH374IS+++CKNGjWifPnyODs7q2JWpEgRvLy8aNSoEc8//zyvvfYakydPZsGCBWzatImDBw9y6tQprly5woMHD6xqC960tDQSExOJjo7mxo0b/Pvvvxw+fJitW7eyePFiPvjgA15//XW6d+9OkyZNqFKlitoDojSCSpcuTb169ejRowcTJkxg2bJlBAUFERERkel3ahseuYnyvsDAQIQQ6loL+Z3fpdBLLMUuhF7raS/H5vMHW/HAV/JG69at1TXv8zqMxlZ1dn7v4cOHXLhwgcDAQJYuXcrUqVMZOnQoXbt2pWnTpnh7e1O8eHF0Op0qikIIdDodxYoVo0yZMlSpUoUGDRrg4+ND+/bt6d27N/369cPf359Ro0YxZcoUJk2axKxZs/jiiy/46quvsjy++OIL5syZw6RJk5gyZQqjR4/G39+fAQMG0Lt3bzp16oSPjw9NmjShWrVqlC1bluLFi6u9F9qjaNGiVKxYkYYNG+Lr68v//vc/Jk2axHfffceuXbs4c+YM9+/fzzK+jOM2r+snpZKcNGkS5cqVK7D6UAq9xFLsQujlDnUFgy2slqdk8NmzZ+Pp6Vmg+9Gb6lbPSXwlJycTGRnJpUuXOHHiBHv37uWXX37h+++/57PPPmPixImMGDGCAQMG0LNnTzp16kTbtm1p3LgxderUoWrVqlSoUIGKFStSoUIFihUrhpubG0WLFjV5uLu7U758eSpWrEjFihWpXLkyderUoWHDhjz33HP4+vrSq1cv+vbty7Bhwxg/fjyzZ89m4cKFrF27ll27dnHs2DEuXLjA7du3zU5JNEduDg/kBo0aNaJfv35AwYirFHqJpdi80Cvd89LTPv+xBateCcuRI0cQQnD8+HGD89aCqUaA4nmeV+UvKSmJhIQEs4cph7bcQPlW47F/axBzc0RFReHi4sLy5cuBgvFHkUIvsRSbF3q5Cl7BYise+AkJCRQrVozPPvsMsD7Hweyi9WQ3no6mFU7tPbkpoJl502cWBmvME9lBqV9+++03hBBcuXIFKJj6RQq9xFJsXuhBetoXJOasemsSUiWMnTp1ol27doD152mJdaDk47feeotKlSoVaFik0EssxaaFXnraWwfWPlavZPLvv/8eZ2dnk+vWSyTm0Ov1lC9fnjFjxgAF14iVQi+xFJsVerkKnvVgC2P1kL7wiqura55Ns5PYF0r+3bdvH0IIddvagsrXUugllmKzQi897a0LrVVfuXJlq7PqlfzSu3dvGjRoAMi8IskcJc/079+fmjVrFnBopNBLLMdmhR6kNW9NWLtVb7z7mPH+9BKJKWJiYihSpIhVOHFKoZdYik0KvXZNe7lDnfVgCx74ycnJlC5dmgkTJgCy+15iGiVfrFq1CiEEN2/eBAq2jpFCL7EUmxN67di89LS3Lqx9DXwlHG+++SYVKlSQeUZiFqWeadOmDc8995zBuYJCCr3EUmxO6KWnvXVjzR74St4JDg5GCMGuXbsMzksk8F8evnr1KkII1q5dCxR8PpFCL7EUmxJ6ac1bP9Y+Vq/dbrR169YG5yQS+C+vjhw5klKlShEfH1/AIUpHCr3EUmxK6JUMPXXqVOlpb8VYswe+kod27twpK0tJBpR8eufOHXQ6HXPnzgWsI39IoZdYik0JvbKmvbTmrRtbserr169Px44dDc5JHBslj44bN45ixYoRGxtbwCH6Dyn0EkuxGaHXjs1LT3vrR+uBb61j9Zs2bUIIwYkTJwzOSxwTxdfn/v37FCpUiBkzZgDW40wqhV5iKTYh9HJs3vaw9jXwlTz11FNP0bNnT0DmJ0dHSf9p06ZRuHBhHj16VMAhMkQKvcRSbELolUAqY/PS0942sAUP/DVr1iCE4Pz580DB53VJwZGWlsajR49wc3Nj0qRJgHWJqBR6iaVYvdCbs+atxTKUmMcWrPrU1FSeeuopOnfuDMhK01FR0n3s2LG4urpy//59qzMmpNBLLMXqhV6uaW/b2IIH/q5duxBCsHXrVoPzEsdAyY/nzp1DCMG8efMA68sHUugllmLVQq+0qKOiouTYvI1i7R74Sjj8/PwoV64c8fHxVtMQkeQPSh5o1aoVdevWJTU11WrypxYp9BJLsWqhl5729oE1e+Arjclbt27h5OTE5MmTAVl5OgpKOq9evRohBEFBQQbnrQkp9BJLsVqhl5729oOtWPVffvklQgguXLhgcF5inyg+GjExMXh4ePDaa68B1pvuUugllmK1Qm/K076gwiJ5cqzZAx/SK8uUlBRq1qxJu3btAOtxGpTkDdpNjooWLUpUVJTVOeBpkUIvsRSrFXqQ1rw9Ye0e+Er4Dh06hBCChQsXAtYTPknuoqT3vn37EEKwZMkSg/PWiBR6iaVYpdBLT3v7xBaseoDJkycjhODff/81OC+xDxSr/d69e3h4eNC7d2/A+tNZCr3EUqxO6I3H5ocOHQrIzGwPWPtYPfwXFh8fH6pWrUpcXBypqalW1SCRPBlKpdexY0fKly/Pw4cPrbrLXkEKvcRSrE7otTvUSU97+0NJX2u16pWwhIeH4+bmxssvvwzILnx7QUnHjz/+GCEE//zzD2AbYimFXmIpViX0Wmu+SJEicmzeDrH2sXr4L4w7duxACMH3338PWFcYJTnHeFz+q6++AmwnXaXQSyzFqoTe3j3ttd9h3B2sLazKtB/t3/YSB2D9Y/XwX16cOHEiQghOnjwJyErVVlHyV2RkJCVKlFDH5W1F5EEKvYJxXZGTutPa6pn8wqqEHqzb094406SkpJgV64IiLS3NoPIyXuXLGjK6LVj18F942rVrR6lSpdSGpzWksyT7KHk+Pj6eJk2aUKVKFWJiYmyuAW1PQm9cJ2nLvrWki3HdaVzfW0MYs4vVCL12bF7xtC+IBNfr9bnynrS0NJKTk9W/Hz58SGRkpPr36dOnuX37NgCxsbEEBQXx+PFjACIiIjh27Jj67Xfu3CE8PFx9Ni4uzuDdT4I28xq3hvMSY6ter9dbXcFR8l90dDR16tTh6aef5sGDB+o1iW2g5OvOnTvj7u7OpUuX1PO2hLULvbHRk1sNd71er9Z3aWlp3Llzh9jYWCC97jx+/Lhab9+4cYPg4GD12QsXLhAaGqqGKTQ0lJiYGPW9cXFxuZIPrLWxomAVQp+fnvZPso712bNnOX36NJAecVOnTmXfvn3qtWbNmhESEgLAwoUL8fLyIiEhAYA+ffrQsWNH9V0lS5bkk08+AeDEiRPodDoOHz4MwBdffIEQgri4OPXZpk2bqs8+/fTTzJw5E4Br165RtWpVDh06BKSPP77++uvq7x4+fJhdu3apzz58+JDExMRsfW9e9gbYggc+/PfNt2/fply5cjRr1kyNW2sqyBLTKBXcyy+/jE6n4/jx44D15bPsYG1Cb2zhZhe9Xs+hQ4dUw+fs2bOMGzeO6OhoAD777DP69Omj3t+6dWtGjRoFwL1793BxcWHlypUA7Ny5EyEEly9fBmD69OnUqlVLfbZRo0YMGDAASNcXIQSLFy8GYO/evbi7u6srYc6dO5fmzZur8TljxgwDP45169apjcTk5GSio6Oz/f0F3RtgFUJvypp/kt/NyXOxsbGqoN69e5fZs2erXbRLly6lRo0aqjB27txZFevU1FQaN26sZpqwsDAGDx6shv3EiRMsXLhQbWmePHlS9fAFOHPmjJrRExMTuXz5siogd+/e5dSpU+p3nD17lmPHjqnPbtiwQW21RkZGMnnyZDUDbt26ldatW6u9A4MGDaJt27bqs1WrVmX69OkAXL9+nYEDB3Lx4kUgvRCdPXs2R5n3SbCFsXr4L3+eP38eNzc3unXrpp63xvBK0lHK3jvvvIMQgr179wLWN0SUXQpC6LMrTmlpaTx69EiN83379rFgwQL1uq+vL2+99RaQXmcJIVi9ejUAgYGBVK9eXa13V6xYwYQJE9Rnf/75Z/bs2QNAUlISu3btUntDY2JiCA4OVuvOqKgotQ6G9B0Jlb9TUlLYv3+/2jsaERHBihUr1AbGvn37mDVrlhqfw4cPZ9KkSUC6Tnh6eqqOuX/++SeFChVSGwmrVq1i9OjRahyFhoZy69atrCOYJzM+s0uBC73SxaF42ltizeckon7//XdWrFih/naVKlX46KOPgPRMUa5cOY4ePQpAUFAQn332mdptFB4ermYwWyEuLk4VfYD169erVs2lS5do0aIFp06dAuCrr76iaNGixMfHA+ktWqXXQVlgJCkpyeTvGHddZQdbserhv4Ly999/I4RQ10W3ti46STpKHpo9ezZCCNauXQvYrshD/gh9dt+l1+v5+uuvVQNk//79BsI3Y8YMGjdurN7/3XffsWXLFiA9DS5dumRQL9kCjx49Uus/40bCd999R8+ePdV7GzZsyP/+9z8gvSdhwIABanrFx8dz7949s/WGpT0lmVHgQm+8Cl52PO0zE5W0tDSuXbvGw4cPAdi9eze1a9dWreeRI0fSvn179f5ffvlFFbonxXiMJjOnOGNr0Pj/mXmSGmcErV/Bk4yzR0REcPLkSfXdY8aMYezYsUB6y7lo0aJqi/bmzZusWrVK7Q0xJrvWrtaqr1y5slWO1Sso6fnHH38ghFAbpSC78a0JJS1mzpyJEIJvvvkGsG2Rh7wR+syMpNjYWMLCwtTro0aNUsUrKSkJb29vtT64desWy5YtU8e/nwTjujMlJSXTutM4/FnNbjJ2qNZey61x9jNnzhAWFgak9zK0bt1a7ZVYs2YNrq6u3L9/H4ADBw4YDK8akxsNuQIXesiep31mwnHy5Ek10z98+BBXV1d17eoTJ04watQooqKigJwVdmt3sLAES2cKJCcn8+uvv6pjYTt27MDV1VXtBluyZAkBAQFmnzf3O7biga+ghGv79u0IIejZs6c6tGONPRGOhDZfjxkzxq5EHnJP6M3FRVJSEjt37lTL9PLly9HpdGrd+e2336pj1pAzXbDG2T85xTjMlmpDeHg469atU+uNl156STU+9Xo977zzDn/99ZfZMFhSzxSo0GflaW/ud2/dusXatWvVLuYePXqo49Cpqans27ePO3fuZCsMedFNYqvkZP5+SkoKDx48UO8fN24c/fr1A9IbBX369GHbtm0mnzVX6K3ZA1+LUmgOHjxIkSJF8PHxUb3x7UFQbBElP6WmpjJgwAC76a7XYqnQZ1aW/vrrL3bv3g2kW57Ozs6qo9vt27cJDAzM9kwke4nn3CCzHltj4uLi1J6Q2NhYmjRpoubdgwcP0qNHD9X6Nya7+lVgQq/1tM9qFbzU1FQOHDigdoVs27aNQoUKcfPmTSB9+tm9e/fM/pbMgLlDdjNVfHw8PXv2VMfkAgMD6d27tzqcYoxSkdjCWL2CkqdCQkIoW7YsderUUS0hmd/yFyW+4+Li6Ny5M05OTmpXqD2lRW5Y9NHR0ezcuVM1kvz8/OjQoYP6nhs3bqiObaZ+357is6DIiT/TwYMH6dKli+oLMHHiRNWZ2tR7MzPMoACE3pQ1r9fr1QDp9Xq1FaPX6yldujSzZs0CICEhgfv375sNl/SGzh+y22Ldu3cvnTt3Vue+LliwgI0bN5q8V+uBb+0oeTU8PJynn36acuXKqTveyQoxf1DiOSIigsaNG1OsWDHVQSy31sSwFrIr9MZC8ujRI9Vi3Lt3r8F0tOjo6Eyd4qy5sW1PZLcunThxIlOmTAHSe2CmT5+uGsCZUaAWvbGnvZbPPvuMsmXLql6O165dM5sh7WHs3N7IrILo2LEjY8aMAdKt/xs3bqjCrlREy5Yty/I91oASvqioKHx8fNDpdOqsDu11Se6iLfOBgYGUKlWKatWqqV7f9tjQMif0WdV9DRo04I033gDSez1CQ0MzdWaWWA+ZjclfvHgRLy8vgoKCgPRp2doufmOHRshnoVd+VLvffHJyMtOnT2fnzp1A+spxGzZskBnSDjCVWZX027ZtGy4uLurqVZDeELB2D3wtyrelpKSoTmAjRoxQu0DtUXQKEm1eUjzre/XqpfpJ2GvjKjOh13arX758mbFjx6rx8euvv6pTho2xhfIl+Y/Meqv79OlDq1atzD4H+Sj0yruioqJwd3fn3XffBdIduJ555hm+/PLLTJ+T2BeRkZFs375dFfXVq1czf/58hBD8+OOPgG0IpTZ/rlu3jkKFClGvXj3Onj0LyOGk3EDbJX379m06deqEEMKgzrBXkYfsd90HBQVRs2ZNg8azFpkP7ZNjx46peeLGjRssXbpU7QVXekyHDh2aP0KvFNQPP/wQIQRNmzZVV2bTYskCLBLbJjY2Fi8vLxYtWkTXrl3x8vKy2tXyzKHk2dDQUJo1a4aTk5M6DKG9LskZ2njbuXMnnp6eeHt7q8tGO8LwnVbodTodQUFB6rkff/yR//3vf2adme25ASTJyNatWylevLi6Lo3CkCFDaNCggcG5XBd65T3R0dEUL16cnj170rdv31xbsEZimxg7DkH6IhK2NFavRetQqiy/6ufnx5UrV9R7bOl7ChJtT8j9+/d54403EELw0ksvqbM4HKXxpOSZ06dPI4TgxIkT6rUffviBAQMG2FzDWJJ7GDfoFE/9uLg4tUGcLxa9UmjHjBmDTqcz2JFNIlFQ1s328PCgRo0aJCUl2ZwwasP722+/UblyZXQ6HQEBAaowye588xj36C1btowSJUrg7u7O0qVL1fO2li+eBK1F7+TkxMaNG9m1a5dDxYEk5+zatQtnZ2ciIiJ48803qVu3rsH1XBV6pVILDg5GCMHIkSMBbMbhSpI/aB33tm7dahOr5WWG8i2JiYnqcFXNmjXVDVZALtqkxVjgg4ODadOmDUIIXn/9dXUpa0foqjdGyUsnT56kSJEi9OnTBy8vLx48ePBES19L7BOlfCQmJqoW/YgRI/LWolcK79SpU3F2ds7WmvYSx0XJF61bt6ZSpUrqGvy2mF+0FfD58+d5/vnnEUIwcOBArl27pl4zXtPbkTAW+AcPHjB27FiEEDRq1IiDBw+q12yxwZcbGI/RHzx4UF2eViLJipSUFF566SUaNmxocD7Xu+6vXbtG4cKF83S/eYl9oOSN/fv3I4RQV++yRaFX0ArUL7/8QoUKFRBCMHz4cM6fP69ecyTnKWOBV7ZdLlq0KEWKFGHevHnqNUcf6lC+XRmjP3LkCCDrUUnWpKamEh0djYeHB88++6zBtVwX+p49e+Li4pJhTXuJxBRaq97b21tdttOW0YpVfHw8c+fOpVy5cggheOWVVzI4ptpjt74i7trvCg8P5+2338bFxQU3NzemTp1KRESEel2K2X9xEBISgk6nY/v27bLLXpItlDzSv3//vLfo69Spw/PPP2/wwxKJORQx2LJlC0IIgznpto7WitXr9SxevJhKlSohhODFF1/MsMCJsiCKLYu+qbXSL1++zLBhwxBCUKJECWbNmqUu9AKO201vCiXfnzlzBiGEOpxhD+VBkrcodcewYcPyfnpdz549qV27NiAzpyRrlEp+9uzZODs7m93ByZYx3g97xYoV1KhRAyEE9evXZ968edy6dSvDM7Yg+orlbizWDx8+ZPny5aqTXbly5Zg7d67BXua28H0FRUxMDK6urixYsACQjSFJ1ih6W69ePV555RWDa7ku9Js3b0YIwa+//grY36YTktxDyXMxMTGULFmSnj17Gpy3N4wr6x07duDn50ehQoXQ6XR069aNX375Rd0YyPhZaxBG7VKspvbu/uOPP+jbty9FihRBCEGnTp1Ys2aNwW5p1vAd1owSN/3796dixYokJiY6vO+CJHOUumXXrl0IIQxm/EAuC70yJv/cc89RokQJdYtZKfYSY7QV16uvvooQQt2hyd4rNGPBj4qKYsmSzPsA+gAADSVJREFUJTz77LMIIXB3d+eVV15h7dq1XL9+PcPzihWt7ASZFyKgFXTld0z9xt27d9m+fTtvvvkm5cuXRwhBnTp1+PzzzzOEXQp89lDi6ObNm+h0Ot58801AOipKTKPoa1RUFGXKlKFHjx6AYY96rgs9pO+4U65cOWrUqKEWdplJJQpaoRs8eDBCCJYsWQLYv8hrMdXlfenSJWbMmEH9+vURQiCEoFatWowaNYpff/2Vu3fvZvrO1NRU9Hq9Ks7aQ/H0Vw7j63q9PsvhNmWv8wkTJtCwYUN0Oh1CCKpXr864ceMIDg7OEB7Z7ZxzlHLw888/I4Rg3Lhx6jUZnxIwnM1y69Yt6tatS/Xq1YmMjMzgCJ9nS+BeunSJihUr4uHhoXbjg2zVOzLaCio0NJQOHToghOC7774DHNenw5SHOqQX3vXr1zN8+HCeeuophBA4OTlRr149+vXrx4wZM9iwYQOnT582cG7LDR4/fsz58+fZtm0bn376KYMHD6Z58+a4uroihMDLy4uBAweyfPlyg2V/FWQ5f3KU8rBy5Up19747d+6o16XgOybG01V37txJqVKlqFq1qtqLblz28mRTGyWDXr9+Xa3MBw8ebOBw5MgLhzgSxpkyOTmZ7777DhcXF0qUKMGWLVsAWWkpZGYBX79+nTVr1vD666/TsmVLypYtq1rULi4uVK5cmfbt2/Paa6/x3nvvMXPmTL755hvWr1/Pnj17CAoK4vDhwwQFBREYGMimTZtYtGgRc+bMYcKECQwZMoQuXbpQrVo1ChcurPYolCxZksaNGzNo0CAWL15ssB6AFlmmcx8lL+zevZsKFSpQvHhxVq1aleEe2aiyf4zr0nv37qn7Qvj5+akrSpoqg3m2H732x77++mucnJzQ6XRMnDjRoPvRnDUjsW2MBSstLY1Vq1ZRpUoVhBAMGDAg04wpMe/Rrr0eGRnJ33//zapVq5g4cSK9evWiSZMm1KxZk/Lly+Pu7o6zs7PaGHB2dsbFxQUhBDqdjqJFi1K2bFlq1KhBo0aN6Nq1K++++y5LlizhwIED3Lp1y6yPjbU4CNo7Svo/fPiQ1157DSEEDRs2ZPPmzRnuk2XJvlDqAG26Pnz4kI8++gg3Nzfc3d3Vrb6V+02RZ0Jv/E5lsQwhBK6urowaNSrDwiH2MI/YkTFljd67d4/58+dTrVo1hBC0adOGffv2qdelJZ99tMKf3Qo9OTmZ+/fvc/XqVcLCwrhy5Yp6REZGkpiYmGe/Lck9tHF+5MgRunTpogr+Tz/9ZDBtEaTo2zLmGvgXL15k3LhxFCtWDCcnJ6ZMmaIuj5zV4nR5KvQK2gBfvHiRUaNGqdNvnnvuOVauXMm9e/cMnjHVkpFYF+bSSK/X8+eff/Laa6+pXcudO3dmz5496j3SOTN30HrHP6mFra1g8sqbX2I5xivkHThwgBdeeAEhBEWLFuXtt9/O4AwJsufFFlDKsHFdGhsby6ZNm/D19VWH0SZOnJhhGDwr8kXolfcbb2ixcOFC6tWrpzoZde/enbVr15pcNEUbETLDFgxaQTEmKSmJQ4cOMXr0aMqWLatmyrFjx6qr3UHGykqS9yitfVOHxPYwrgPDwsKYNm0aFStWRAjB008/zZQpUwz2slfQNuZk+hccmdWlsbGxbNu2jQEDBlCsWDGEEDRv3pxVq1ZZvB5Fvgm99neMP+7MmTNMnz6dmjVrqg5APj4+zJ49m6NHj5KcnGz2PVL884bsdNVev36dn376CT8/Pzw9PVXL4uWXX2bbtm0G69ZLgZdIchfjjZFSU1PZt28fw4cPp3Tp0ursiMGDB7N+/XqDfQW05EZvkMQ8WlE3VweGhITw1Vdf0alTJ9zd3RFC0LRpUz7//HMuX75scK8l6ZTvQq/9PVOtmVOnTjFz5kxatGihir6npycvvPACn376KX///TePHz82+968XkjEnlCsOuM4M3fv2bNnWbZsGUOGDKF69epq+lSrVo1Ro0axffv2DGkjh18kkrzFVF2q1+sJDAzkvffeo06dOqrzZZMmTRgzZgwbNmzg6tWrZt9pLE6yHs0cU3WpuThLSkri5MmTfPvtt/Tv3x8vLy/VSPL19eXrr7/OIO7m9DK7FJjQazE3pej+/fts27aNUaNGUbduXVVYXFxceOaZZxgxYgQrVqzg+PHjPHr0KNPfMCVojiBAxiucKYuiZJbeiYmJhIWF8euvvzJt2jS6du1KyZIl1fgvW7Ysffr0YdGiRVy6dCnD85l5ikskkrzDXF1648YNVq1axaBBg1THWCEElStX5sUXX+Szzz5j9+7d3L59O9P3G9ejjtQQMPaHyc4CUwkJCZw/f57169czfvx42rRpg4eHB0IIihQpQvPmzRk/fjyBgYEZlr7OzRlpViH0WjLzvL937x6BgYFMmzaNdu3aUapUKTXDCiGoV68efn5+fPrpp6xdu5Zz585luZKYqd82dSiZuaDGNrW/bW5ls5wKbFxcHFeuXOGPP/7gm2++YcSIEfj4+FC0aFE1Tt3c3KhXrx4jR45k/fr1GVqaCrLrTyKxLjJbk+HmzZts3bqVsWPH4uPjQ4kSJdQyX758eTp16sT48eNZunQphw8f5ubNm9k2jIydOo1XZrQG/xDjutRcfZrdcMbGxnL58mV+//135s6dy5AhQ2jatKnaDa80qnr16sVnn31mtmc6r2aeWZ3Qa8nOPOLQ0FB27tzJ7Nmz6dGjB7Vq1TIQfyEEVatWpUWLFowYMYJp06axbNkyjhw5wtmzZ3Nt/3NzomvpkRvpkZqaytWrVzl27Bg7duxg1qxZjB8/ns6dO/P000/j5uZmEE8VK1akVatWjB8/nhUrVhASEkJcXFym3+sIvSISia2TVV2q1+u5dOkSmzdvVnvxqlWrRqFChdT6oVSpUjRt2pS+ffsyadIkvvvuO3bt2kVISEiu7TqZmQFTkHVpUlIS4eHhHD9+nI0bN/L555/z5ptv0qVLlwx1afHixWnQoAGDBg3iq6++4sCBAwYrGmrRzlzKSw22aqE3Jrseo9HR0WrX89dff83LL7+Mr68vFSpUUBcLUY7ChQtTsmRJvL298fX1ZdCgQYwcOZKAgAA2btzItm3b2L17N0eOHOHGjRs8evSI2NhYEhMTTToJ5japqakkJiYSHx9PTEwMkZGRBAcHs2/fPn777Tc2b97M4sWLeeeddxg8eDB9+vShVq1alC5dWvXYVA5nZ2eKFy/OM888Q69evfjwww9Zs2YNx48fz7LnQ1rsEon9kN269OHDh5w7d45ff/2VgIAAXn31VVq1aoW3t7dBz5+TkxOenp7UrFmTZ599Fj8/P0aPHs3MmTP56aef2LJlCwcOHODEiROEhoYSFRVFXFxcgRgKycnJxMTEcOfOHc6dO8c///zDnj172LBhA9988w3vv/8+Q4YMoWvXrjRu3JgqVaoYWOaK31itWrV4/vnneeutt1i4cCH79u3jxo0bma5NUVCzx2xK6E2hHX/OTqZJTEzk+vXr7N+/ny1btjBjxgxGjx6Nv78/Pj4+eHt7U6ZMmQwNAu2h0+koVKgQ7u7ueHl58fTTT9O6dWuee+45OnbsSMeOHencuTO9evXK8ujduzfdunWjY8eO+Pr60q5dO1q3bk2DBg2oXLkynp6eFCpUKNPwKFPZKlasSL169ejbty8jR45kwoQJrFq1ir1793LmzBni4uKy7NqXTjgSiWOS07o0ISGBq1evcvjwYX7++WcCAgJ499136d+/P23atKFOnTqUKVPGoFdAexQpUoQyZcpQrlw5vL29qV27Nk2aNKFVq1Z06dKFF198kd69e/Pyyy8zZMiQTA9/f3/8/f156aWX6N27N3369KFdu3b4+PhQv359atWqRcWKFSlfvjyenp7qapHGh7u7O5UqVaJx48Z07twZf39/3n//fRYsWMCOHTsIDg4mMjIyyx1Ztb4M1lCP2rzQm0LrAWnJ2DWk75F+5coVzp07x7///stff/3FmjVrmD9/PgEBAcyYMYPp06czZswYBg4cSPfu3Xnuuedo2bIlTZs2pVmzZjRr1ozGjRvToEEDk0fDhg3Ve5s2bUrz5s3VxkL//v0ZOnQoH374IR9//DFz5sxh7ty5LF26lN27dxMcHExISAiXL19Wl5LNSfyY8j+QSCQSLaYWZMqpFf748WNu375NaGgowcHB/Pnnn2zatImlS5fy9ddfM2PGDKZOncro0aMZNmwYffv2pXfv3nTs2JH27durR+PGjalfv77J49lnn6VDhw60b9+edu3a0bVrV3r37s2gQYMYMWIE7733HtOmTSMgIIDvvvuOlStXsn37doKCgggJ+b/27dgGQBCKouj++7kALStQYEVCQaI2Rh/nbAAFl5DP0Uspvdb6+JX2L+doZOivzKEbk+ittYg9mG+SO07GAu9Z/eq5+yLwZWNdKefolqEHgF0IPQAEE3oACCb0ABBM6AEgmNADQDChB4BgJ5hzTCbjsgR9AAAAAElFTkSuQmCC[/img][br] [br]What is the height of the cylinder in terms of [math]r[/math]?
What is the volume of the cylinder in terms of [math]r[/math]?
What is the volume of the cone in terms of [math]r[/math]?
What is the volume of the sphere in terms of [math]r[/math]?
A volume of the cone is [math]\frac{1}{3}[/math] the volume of a cylinder. The volume of the sphere is what fraction of the volume of the cylinder?

IM 8.5.20 Practice: The Volume of a Sphere

[size=150]A cube’s volume is 512 cubic units. What is the length of its edge?[/size]
[size=150]If a sphere fits snugly inside this cube, what is its volume?[/size]
[size=150]What fraction of the cube is taken up by the sphere? What percentage is this? Explain your reasoning.[/size]
Sphere A has radius 2 cm. Sphere B has radius 4 cm.
Calculate the volume of each sphere.[br]
The radius of Sphere B is double that of Sphere A. How many times greater is the volume of B?[br]
[size=150]Three cones have a volume of [math]192\pi[/math] cm³.[br] [/size][br]Cone A has a radius of 2 cm. [br]Cone B has a radius of 3 cm. [br]Cone C has a radius of 4 cm. [br][br]Find the height of each cone.
The graph represents the average price of regular gasoline in the United States in dollars as a function of the number of months after January 2014:
[img]data:image/png;base64,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[/img][br][br]How many months after January 2014 was the price of gas the greatest?
Did the average price of gas ever get below $2?
Describe what happened to the average price of gas in 2014.
What is the volume of each sphere?
Sphere A: radius of 4 cm
Sphere B: diameter of 6 cm
Sphere C: radius of 8 cm
Sphere D: radius of 6 cm
While conducting an inventory in their bicycle shop, the owner noticed the number of bicycles is 2 fewer than 10 times the number of tricycles. They also know there are 410 wheels on all the bicycles and tricycles in the store. Write and solve a system of equations to find the number of bicycles in the store.

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