Lesson 13
The Volume of a Cylinder
Problem 1
- Sketch a cylinder.
- Label its radius 3 and its height 10.
- Shade in one of its bases.
Solution
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Problem 2
At a farm, animals are fed bales of hay and buckets of grain. Each bale of hay is in the shape a rectangular prism. The base has side lengths 2 feet and 3 feet, and the height is 5 feet. Each bucket of grain is a cylinder with a diameter of 3 feet. The height of the bucket is 5 feet, the same as the height of the bale.
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Which is larger in area, the rectangular base of the bale or the circular base of the bucket? Explain how you know.
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Which is larger in volume, the bale or the bucket? Explain how you know.
Solution
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Problem 3
Three cylinders have a height of 8 cm. Cylinder 1 has a radius of 1 cm. Cylinder 2 has a radius of 2 cm. Cylinder 3 has a radius of 3 cm. Find the volume of each cylinder.
Solution
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Problem 4
A one-quart container of tomato soup is shaped like a rectangular prism. A soup bowl shaped like a hemisphere can hold 8 oz of liquid. How many bowls will the soup container fill? Recall that 1 quart is equivalent to 32 fluid ounces (oz).
Solution
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(From Unit 5, Lesson 12.)Problem 5
Match each set of information about a circle with the area of that circle.
Solution
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Problem 6
Two students join a puzzle solving club and get faster at finishing the puzzles as they get more practice. Student A improves their times faster than Student B.
![Coordinate plane, x, number of days of practice, 0 to 11 by ones, y, minutes to complete a puzzle, 0 to 7 by ones. Line l through 0 comma 6, and 7 comma 4. Line m through 0 comma 5, and 7 comma 4.](https://staging-cms-im.s3.amazonaws.com/1qYZaJK29kjGo2CCNcCFWHQc?response-content-disposition=inline%3B%20filename%3D%228-8.5.C8.PP.Image.105.png%22%3B%20filename%2A%3DUTF-8%27%278-8.5.C8.PP.Image.105.png&response-content-type=image%2Fpng&X-Amz-Algorithm=AWS4-HMAC-SHA256&X-Amz-Credential=AKIAXQCCIHWF37H2AMFB%2F20240722%2Fus-east-1%2Fs3%2Faws4_request&X-Amz-Date=20240722T155213Z&X-Amz-Expires=604800&X-Amz-SignedHeaders=host&X-Amz-Signature=9c854bbd6dab6cd5eb1e094848fb239575e53624feb67e4ec07761a2d5044b3a)
- Match the students to the Lines \(\ell\) and \(m\).
- Which student was faster at puzzle solving before practice?
Solution
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(From Unit 5, Lesson 8.)