IM 8.5.22 Lesson: Volume As a Function of . . .
A cylinder and sphere have the same height.
If the sphere has a volume of [math]36\pi[/math] cubic units, what is the height of the cylinder?
What is a possible volume for the cylinder? Explain your reasoning.[br]
Fill in the missing volumes in terms of π. Add two more radius and volume pairs of your choosing and answer the questions below.
How does the volume of a sphere with radius 2 cm compare to the volume of a sphere with radius 1 cm?
How does the volume of a sphere with radius [math]\frac{1}{2}[/math] cm compare to the volume of a sphere with radius 1 cm?
For the following questions, a sphere has radius of length r.
What happens to the volume of this sphere if its radius is doubled?
What happens to the volume of this sphere if its radius is halved?
[size=100]Sphere Q has a volume of 500 cubic centimeters. Sphere S has a radius [math]\frac{1}{5}[/math] as large as Sphere Q. [/size]What is the volume of Sphere S?[br]
[size=150]Three containers of the same height were filled with water at the same rate. One container is a cylinder, one is a cone, and one is a sphere. As they were filled, the relationship between the volume of water and the height of the water was recorded in different ways, shown here:[/size][br][br]Cylinder: [math]h=\frac{V}{4\pi}[/math][br]Cone: [br][img]data:image/png;base64,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[/img][br]Sphere: [br][img]data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAOUAAAIrCAYAAAAQtF77AAAXuUlEQVR4nO3bXZKrOLeEYUWc2zMXjUgDYjYaDFPp6/VdAGn+jcvscqr8PhFE9C5TsstJIoHdKQBYSZ9+AQCWKCVghlICZiglYGa3lP//f4mNje2G7dZSol3k54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DxQSgj5eaCULaklUkqzrUS9cXjy80ApWzUVtNxXS/LzQClbNZYyd/1tQ5Kfhz9SyhplXNLdOHHcazGz9dHl9LNSzZawj791Gi/HOx39UX56Pe8tpfsuD+PkLl75E2pJN64YVu/jj/626Vj8+ftBKX/FGLYOuMfr/fHBtFm+jmO+eFDPfbKUKteL41wqZd9FThdOWuPfMg2lE8WrJ7vp+X6YLaX8Df9gqbl3Rh4O0J/Plp8s5U/dV8pplrzj73hvrM+W8nQptjzrP86keyFsS7m3HNIY08+m589dVJ0VH4/Pn3NbqNls92SGml7L3t84javXW+rqbz0IdudsPI3x0/K/XcrF3eHt6+7n7/HqBLq/fJ0dCylFKp3+Pf3uvJSL9+1xIIyFfPae7qw01iccjbX+W7eTwfRafjJJfHimnL3pO2/i8KNVMLtF+GEpdwM73vQGH/3eQTG3M9jONeXm447tAbY+qDfP9+Yd2fdKefy6h93O39NtXie5z97Lo3E19tVS7i05N6uA1Yn4ZMx3TpAfX74+DrTxj1q/ETuz6fzgHH72fimnN+8R8hT8Y+z1Po83/Gz5vLeUOS/lZha4ugz6xLXMldc9n2H0Upf5bPI6zX2vlDvF2ZzoT5ave5cYZ6V8/LH7s+UblywfL+X6DVsf8PsH5roo75byEdbp75Ua52fLvRBeLeVsv1ev1z5ayuPXvZnhd2aY9fu+yWr+9+2Vcm9W/oelfDzdwQm56VIuDtC6ubVPKSklpbzm3ruvuhYqJxfbP1y+KoidG0g/KuXOdfDTP299QPyjUn70mvLkdevfx6U4XM5eXb5eKuXJjZcXrymflbLpa8rBcvZZ/iEnF/zrz+jShZsxb5cyjm9uHNzouXL39Y5Sbp/nNf+slCcZHq9szlYkL5by0p3yC3dfXyjlOx9PmZRy7wbL0eN7xT0/W2nc7ugW94ulXPzudim28+JXr/nflNLmc8qD1713p3TzkdCiMMsyle6Hy9fFazoq5c5lxo9L2fLnlF/jzg+mj3zoGz3/UN8v/5LNnfq73fUlD77R04h/8H91PHzwu6//zPGS995vRu095zvvI999xY288tsvpeXXKG9GKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DzcXko2Nrb3t9tK+d9///1oMHggPw8/zYFS/kHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DxQSgj5eaCUEPLzQCkh5OeBUkLIzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFDKC/ouR0pp3ErUT7+gf6Tt/GoUZZQid/2nX9CPUconhkI+ilhLipS7aDfyY+3mNxRSRey7yClFafTsSSlPDWEvwm088DOt5td3eXOibPnkSSnP1BIp5ViuhProctvLoyNt5jfkkdZnyVqavdSglGd2gz04CP6ANvM7OEnunlDbQClPrK8nx59SSiur60n9mFK+NZgtlq8NYPk6+Y5ScqOnCdzoGXxJKcdw+UjE23ii5CORGwdzNxRz3P5oISMaz28s4pRTq4WMoJSYIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DxQSgj5eaCUEPLzcHsp2djY3t9uLSXaRX4eKCWE/DxQSgj5eaCUEPLzQCkh5OeBUkLIzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQn4evLmUtKVJ6bKUe7dlHl5f75q5fjxYlzfcpcTicqdbyW5pldBxkE762lLWkSLmL/vGDSCnHpmvjY4uca1mVeCjkvKib8RvQUn5LQyFLHd93Svn+YL9vCHE52w3FupbnqoR9F3ld6Fqamy3bye8YpbxpsE/ou7yYGYd/XyvRsOyd7zsunTQzjv9u7OBoKb8jlPKmwT6m7yJP14DPlprzfQ9CH4p9dM3pr7n8dlDKmwb7hPXMOMx+B9eUu787X+quZ8bxpg/XlL+OUt402K8bZ71ldq8tOec3cnaXvrvP4a2Z/E5QypsG+3V7N2bitTumm1Jufm97R9ZdM/mdoJQ3Dfb71jdmYjOzLW7m1LqcBdcfiYy/Oy/gKzeOXLST3zFKedNgn7H9QsDmGnEs1fpLBrtfNJjfCOLLAx9DKW8aDB7IzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DzcXko2Nrb3t1tLiXaRnwdKCSE/D5QSQn4eKCWE/DxQSgj5eaCUEPLzQCkh5OeBUkLIzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTn4XtKWUuklB5b7qJ/sk+pZ8Ol5Xjrna88nxnr/E710eV0OTt3X1LKGiWVeOQ0hjgrSt/lSPN9+i7yUbh9F6XrF//OKUXWz54/nyPf/M71XZ6996ETYqvF/JJS7qglUsoxZFmjLEo17XK1SGPpzqfW2fN5aiq/UxfyMPblpZxms6GU6ww3s+eBYb8nhVs8n6em8js1lHJ9km3F15ayluWZdLhGnJdmKOpxkabHr82m6+dz1FJ+p/ousvmq5Mx3lnJ31lrfLCjRdfna8nW8hjk8MzcwS0Y0lN+ptmfJiG8s5eVru3EmvDi7HS51G7iWnDSR36m2ryUn31XKFwpy6Tpxs/+qlA0VMqKB/E79jUJGfFEpXynZ9BnkPN/F7/c16nyczUcir5fagXN+515b1bj7jlKuP8jf+5B5LNbRjZuhqEPJhsItx9n7nOz0+QzZ5ndq+8WBlr6wsec7SolLyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DxQSgj5eaCUEPLzQCkh5OeBUkLIzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw83F5KNja297dbS4l2kZ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DxQSgj5eaCUEPLzQCkh5OeBUkLIzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk5+F7Stl3kVOKtNhK1O2O0eWzx0e1rMZKkXIX/cvP58M6v1M1yuq9Ls5v9BPfU8palqU52udioH2XI53teOX5zFjnd6LvSnT9/N85UsqLn7Xka0r5tER9F/mFmayWFPkk9afPZ8g5v5eMq5TG3n75mlLWslzerAs1lKzOlq7ppFT9cr+dA+DZ8zlyzu+6MZvGVilzX1PKhel6UE2arklmS57xbHulTMNy6WTfzfN5aia/PbNr/BZOgGe+s5QxFWlcrh4sdxb7PFHL+dn5lbE+paX8zgyrFK4p3xrsI2p5BHdDKZ/uO38+U03ld2pcwpqvTI58bSmXJRpCXC97+i5fvjZhpnRCKd8e7N/ro5+3Ze96cT2TrWbPxW32vl+Wb/NRyoXnM+Sb37m+1li+3Xwk8vZg/9zOB/27J9HVfvN95tcp042dx7Y6AK4+nxnb/E5t74S3XMiIbyklLiE/D5QSQn4eKCWE/DxQSgj5eaCUEPLzQCkh5OeBUkLIzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy83B7KdnY2N7fbi0l2kV+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DxQSgj5eaCUEPLzQCkh5OeBUkLIzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk54FSQsjPA6WEkJ+HLyplH11OkdK05ej6+cNd5HTy+Fwts/2WW6nrp52Nu3nQi3d+V9UoKUXKXRzF5+5LSjkWclaKvsuRUonpJ7U8/nv4d1o8/lQtm/1fHuPDfPO7asi5lEIp3x3s3xvOnouJqu8iP50NTx5fGA6GPNu577L9zLjmm98103ved5lSvjvYb1jPWrWcLXHGJdDVUm1myRol5ejqckns3lHn/J6aZUApbxjs18yvBXcaMixpXy3QdpbU88wOjGHsqzPvZ9jnd2g8CY7vLaW8YbDfsJwZp5s+R9d7zx5fDLzZb329uhjTeLp0zu/YwaUDpXxvsH9u9/pwWKLm44vKJ48f70Mpf9HJnfAWLhn2fFEpXy3J81Luly8ObiLtLHPN2Ob3ImbKGwb793Zu3Kxmz1qX1VrfGNpeE56Xdn0j6bDARnzzew2lvGGw3zEWc/fLAevHtteTQ0lnJb7wGeSwz/54jrzzu45S3jAYPJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DxQSgj5ebi9lGxsbO9vt5YS7SI/D5QSQn4eKCWE/DxQSgj5eaCUEPLzQCkh5OeBUkLIzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM/D3y5lLZFSipRydP3Z4yf7RET0XeSUIpX65Hm2m35lvU/u4ujpPsUuvxfUsn3v82Gg3v5uKWsZDvy+i7xXuFoWRey7HCmV2NauRkk5SsnHpTx6fo1XoyzG7qPLfsW0yu8lw/v5SjzO/m4pJ7ulHEJcnklrlJ2zay3Dz2o5mSm3T7oz/srqpODAMr9LhhOn03v5ju8s5bgcXXdsXby+y5rNXirlYpZ8Y59fZpnfFdPlhTav9/VVX1zK7Zm1ltmSsu8iz8K9XsoLs+RL4/0ey/xeNl4aNDxzfmcpD5aOj1IOS9l5Zy6XqNFZMsI0vx/ZvxRpxXeW8snydbjps3839fwMfOFgMLyWnFjm9yPjbGm2ErnqO0v5wo0ePXphpjy+g6tBbAsZYZrfjzBTvj3YP3Vw/TgU6MpHIoPdm0CLcc8PhO3+fizzu6Dvt3fMHS8PrvraUg4P5ct37NalHIJ/jHt6IFz5coEBy/yemm7seH8x4xV/v5S4jPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DxQSgj5eaCUEPLzQCkh5OeBUkLIzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk54FSQsjPw+2lZGNje3+7tZRoF/l5oJQQ8vNAKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DxQSgj5eaCUEPLzQCkh5OeBUkLIzwOlhJCfB0oJIT8PlBJCfh7+dilriZRSpJSj63ce77vIKUVKKUo9fux0jMXTzfbPXRzt3nd5/zk/zC6/H3hk8DwvV3+3lLUMxei7yHsB9V3kVKJGjbJTkFpK1MW/U6S0/FmsH1cR++hyirTXuloi5RIlU8pbjSfR3GoTZ/5uKSdHpZT9Um53K09m3NVju/vXKClH1198zl9mmd8l0/v66ddxD0p5qZTDPrszX0zL0fUsuh53mD2HMzmlvFPf5UilXr58cEcpTwoyXfs9u/7ru7xzEAzjTsup6cB59pyfZJnfU+OlwuL9PD+JuqOUlwoyBb9/Tbm8nlyOm7t+XMrOf5dS3md58nv8+ORywxylvFyQg/Dj2fL1cSbf3YyWWZb5PUUpJ5Ty2XOcHhTMlHeqZWepulmdtINSHn0kUlfz3uojkWF2nMYdZ8MrH4mcPOenWeZ3xfhxyPqastWPRyjlbkHGGwWLbe9zy/m4q2XqaeMo5e1WX/ZotZAR31BKXEZ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DxQSgj5eaCUEPLzQCkh5OeBUkLIzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk5+H2UrKxsb2/3VpKtIv8PFBKCPl5oJQQ8vNAKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DxQSgj5eaCUEPLzQCkh5OeBUkLIzwOlhJCfB0oJIT8PlDIi+i5HSilSKlHXD9YyPjZuuYv+dJ8c3WaHNrSa31wt35vDnyll3+VIpY7FWpeyRln8rI8ur4pZy+IAGAq+U+4GtJif9F3klCK32sSZry+l7JbyaL+phENJlwdCjdLowdFufjVKwzPjGqWcvFTKcb/x7Fzqepc0zL6NaTW/abXzWLoeXGY0glJOLpZyUbi+i7xzhq6lzYOizfzGS4rFyXFYrbR4YoyglA9XSrneZ3U9+fgxpfw9B5cLB9m0gFJOnpVyL2SWrwYo5eS7SnkYMDd6HOyeBK/eIzBEKScHIQ4fcRyfcdeP85HIB2xWLO2eGCMo5cNeKddfHJht8xPz48sHB19AaETT+Y3FnHJotZARlBIz5OeBUkLIzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4ebi8lGxvb+9utpUS7yM8DpYSQnwdKCSE/D5QSQn4eKCWE/DxQSgj5eaCUEPLzQCkh5OeBUkLIzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy8/D1pey7HCmlx1bqk31KbPaoZfZ4jq7/lZd+uxbzW6vle3P4G6Xsu8i5i0d2NcqqmEMhH0WsJUWa/04tiwNgvX9Lmstvru8ipxS51SbOfHcpdyxLNZR0MXmO4Q8/66PL6wNh+J0WD45286tRGp4Z1yjlSt/lx0y4mgXHPR5FXBT0oZb9ZbC7VvPruxyp1NnSdbWaaQylXFjNfLXsLEWHfVKpYym3Z+jNErcRbeY35rE4OW4vQ1pCKWcWs2QcXR/OSrk7k1LK33VwuXCQTQso5Wi3gCxfG0ApJ3+qlMd3TLnR04Ldk+DupUcbvr6Uw82B4/DWj6+XpkOh+UjkozYrlnZPjBFfXsrNFwcOvgDw7K7e0y8XNKK1/BbGYk45tFrIiC8vJZbIzwOlhJCfB0oJIT8PlBJCfh4oJYT8PFBKCPl5oJQQ8vNAKSHk54FSQsjPA6WEkJ8HSgkhPw+UEkJ+HiglhPw8UEoI+XmglBDy80ApIeTngVJCyM8DpYSQnwdKCSE/D5QSQn4eKCWE/DzcXko2Nrb3t9tKCeBzKCVghlICZiglYIZSAmYoJWCGUgJm/gfppLBuwGpr5wAAAABJRU5ErkJggg==[/img][br][br]The maximum volume of water the cylinder can hold is [math]24\pi[/math]. What is the radius of the cylinder?[br]
Graph the relationship between the volume of water poured into the cylinder and the height of water in the cylinder on the same axes as the) cone.
What does the slope of this line represent?[br]
Which container can fit the largest volume of water? The smallest?[br]
About how much water does it take for the cylinder and the sphere to have the same height? Explain how you know.[br]
About how much water does it take for the cylinder and the cone to have the same height? Explain how you know.[br]
For what approximate range of volumes is the height of the water in the cylinder greater than the height of the water in the cone? Explain how you know.
For what approximate range of volumes is the height of the water in the sphere less than the height of the water in the cylinder? Explain how you know.[br]