IM 8.5.19 Lesson: Estimating a Hemisphere

Here are two shapes.
[img]data:image/png;base64,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[/img][br]What do you notice? What do you wonder?
Mai has a dome paperweight that she can use as a magnifier. The paperweight is shaped like a hemisphere made of solid glass, so she wants to design a box to keep it in so it won't get broken. Her paperweight has a radius of 3 cm.
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[/img][br][br]What should the dimensions of the inside of box be so the box is as small as possible?
What is the volume of the box?[br]
What is a reasonable estimate for the volume of the paperweight?[br]
Tyler has a different box with side lengths that are twice as long as the sides of Mai's box. Tyler's box is just large enough to hold a different glass paperweight.
What is the volume of the new box?
What is a reasonable estimate for the volume of this glass paperweight?[br]
How many times bigger do you think the volume of the paperweight in this box is than the volume of Mai's paperweight? Explain your thinking.[br]
A hemisphere with radius 5 units fits snugly into a cylinder of the same radius and height.
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[/img][br][br]Calculate the volume of the cylinder.
Estimate the volume of the hemisphere. Explain your reasoning.[br]
A cone fits snugly inside a hemisphere, and they share a radius of 5.
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[/img][br][br]What is the volume of the cone?[br]
Estimate the volume of the hemisphere. Explain your reasoning.[br]
[size=150]Compare your estimate for the hemisphere with the cone inside to your estimate of the hemisphere inside the cylinder. [/size][br][br]How do they compare to the volumes of the cylinder and the cone?[br]
[size=150]Estimate what fraction of the volume of the cube is occupied by the pyramid that shares the base and a top vertex with the cube, as in the figure below.[/size]

IM 8.5.19 Practice: Estimating a Hemisphere

[size=150]A baseball fits snugly inside a transparent display cube. The length of an edge of the cube is 2.9 inches.[br][br]Is the baseball’s volume greater than, less than, or equal to [math]2.9^3[/math] cubic inches? Explain how you know.[/size][br]
There are many possible cones with a height of 18 meters. Let [math]r[/math] represent the radius in meters and [math]V[/math] represent the volume in cubic meters.[br][br]Write an equation that represents the volume [math]V[/math] as a function of the radius [math]r[/math].
Complete this table for the function, giving three possible examples.
If you double the radius of a cone, does the volume double? Explain how you know.
Is the graph of this function a line? Explain how you know.
A hemisphere fits snugly inside a cylinder with a radius of 6 cm. A cone fits snugly inside the same hemisphere.
What is the volume of the cylinder?[br]
What is the volume of the cone?[br][br]
Estimate the volume of the hemisphere by calculating the average of the volumes of the cylinder and cone.[br]
[size=150]Find the hemisphere’s diameter if its radius is 6 cm.[/size]
[size=150]Find the hemisphere's diameter it its radius is [math]\frac{1000}{3}[/math] m. [/size]
[size=150]Find the hemisphere’s diameter if its radius is 9.008 ft.[/size]
[size=150]Find the hemisphere’s radius if its diameter is 6 cm.[/size]
[size=150]Find the hemisphere’s radius if its diameter is [size=100][math]\frac{1000}{3}[/math][/size] m.[/size]
[size=150]Find the hemisphere’s radius if its diameter is 9.008 ft.[/size]
After almost running out of space on her phone, Elena checks with a couple of friends who have the same phone to see how many pictures they have on their phones and how much memory they take up. The results are shown in the table.
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ld this information be reasonably modeled with a linear function? Explain your reasoning.
Elena needs to delete photos to create [math]1,200[/math] [math]MB[/math] of space. Estimate the number of photos should she delete.

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