Lesson 15
The Volume of a Cone
Let’s explore cones and their volumes.
Problem 1
A cylinder and cone have the same height and radius. The height of each is 5 cm, and the radius is 2 cm. Calculate the volume of the cylinder and the cone.
Problem 2
The volume of this cone is \(36\pi\) cubic units.
What is the volume of a cylinder that has the same base area and the same height?
![A drawing of a cone.](https://cms-im.s3.amazonaws.com/T3oqzzGTv6xpMFZmZ6kVF62S?response-content-disposition=inline%3B%20filename%3D%228-8.9.A.PP.Image.04.png%22%3B%20filename%2A%3DUTF-8%27%278-8.9.A.PP.Image.04.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T182346Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=4066e4830fafa9633784580d6509ca9971000f6cdadf44ad3535d85eda1e3b68)
Problem 3
A cylinder has a diameter of 6 cm and a volume of \(36\pi\) cm3.
- Sketch the cylinder.
- Find its height and radius in centimeters.
- Label your sketch with the cylinder’s height and radius.
Problem 4
Lin wants to get some custom T-shirts printed for her basketball team. Shirts cost $10 each if you order 10 or fewer shirts and $9 each if you order 11 or more shirts.
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Make a graph that shows the total cost of buying shirts, for 0 through 15 shirts.
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There are 10 people on the team. Do they save money if they buy an extra shirt? Explain your reasoning.
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What is the slope of the graph between 0 and 10? What does it mean in the story?
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What is the slope of the graph between 11 and 15? What does it mean in the story?
Problem 5
In the following graphs, the horizontal axis represents time and the vertical axis represents distance from school. Write a possible story for each graph.
![Three graphs, all quadrant 1, all linear piecewise. First, positive, constant, positive slopes. Second positive, constant, negative slope. Third, negative slope.](https://cms-im.s3.amazonaws.com/VdzDk47438m8JU6WqsS7tHZd?response-content-disposition=inline%3B%20filename%3D%228-8.5.B4.Image.02.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.B4.Image.02.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF3XOEFOW4%2F20240630%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240630T182346Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=e39831b84b78bc828659338b93a615bd459a9c838db6a9213bda73c99d695188)