Lesson 20
The Volume of a Sphere
Let’s explore spheres and their volumes.
Problem 1
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A cube’s volume is 512 cubic units. What is the length of its edge?
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If a sphere fits snugly inside this cube, what is its volume?
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What fraction of the cube is taken up by the sphere? What percentage is this? Explain or show your reasoning.
Problem 2
Sphere A has radius 2 cm. Sphere B has radius 4 cm.
- Calculate the volume of each sphere.
- The radius of Sphere B is double that of Sphere A. How many times greater is the volume of B?
Problem 3
Three cones have a volume of \(192\pi\) cm3. Cone A has a radius of 2 cm. Cone B has a radius of 3 cm. Cone C has a radius of 4 cm. Find the height of each cone.
Problem 4
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.
![Coordinate plane, horizontal, months after January 2014, 0 to 36 by fours. Vertical, average price of gas in dollars, 1.6 to 4 by point fours. Graph shows decline, 3 peaks. Please ask for assistance.](https://cms-im.s3.amazonaws.com/7rLpesrNz3EznoQvjd5iR7Ap?response-content-disposition=inline%3B%20filename%3D%228-8.5.B5.PP.Image.104.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.B5.PP.Image.104.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240908%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240908T002728Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=efa9705cb2a8f0f0cb725b9b3b349869992fee240bea3388292035dd20745189)
- 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.
Problem 5
Match the description of each sphere to its correct volume.
Problem 6
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.