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Unit 5 - Lesson 13 - Grade 8: Illustrative Mathematics

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Grade 8 Unit 5
Lesson 13: The Volume of a Cylinder
CC BY 2021 Illustrative Mathematics®
Grade 8 Unit 5
Lesson 13: The Volume of a Cylinder
CC BY 2021 Illustrative Mathematics®
Lesson: The Volume of a Cylinder

A Circle's Dimensions (Warm Up)

Here is a circle. Points A, B, C, and D are drawn, as well as Segments AD and BC.

1.

What is the area of the circle, in square units? Select all that apply.

2.

If the area of a circle is 49π square units, what is its radius? Explain your reasoning.

Circular Volumes

What is the volume of each figure, in cubic units? Even if you aren’t sure, make a reasonable guess.

3.

Figure A: A rectangular prism whose base has an area of 16 square units and whose height is 3 units.

4.

Figure B: A cylinder whose base has an area of 16 square units and whose height is 1 unit.

5.

Figure C: A cylinder whose base has an area of 16 square units and whose height is 3 units.

A Cylinder's Dimensions (Optional)

For cylinders A–D, sketch a radius and the height. Label the radius with an r and the height h with an h.
6.

7.

8.

9.

Earlier you learned how to sketch a cylinder. Sketch cylinders for E and F and label each one’s radius and height.
10.

11.

A Cylinder's Volume

Here is a cylinder with height 4 units and diameter 10 units.

12.

  • Shade the cylinder’s base.
  • What is the area of the cylinder’s base? Express your answer in terms of π.
  • What is the volume of this cylinder? Express your answer in terms of π.


13.

A silo is a cylindrical container that is used on farms to hold large amounts of goods, such as grain. On a particular farm, a silo has a height of 18 feet and diameter of 6 feet. Make a sketch of this silo and label its height and radius. How many cubic feet of grain can this silo hold? Use 3.14 as an approximation for π.

Cool Down: Liquid Volume

Liquid Volume

The cylinder shown here has a height of 7 centimeters and a radius of 4 centimeters.

14.

What is the area of the base of the cylinder? Express your answer in terms of π.

15.

How many cubic centimeters of fluid can fill this cylinder? Express your answer in terms of π.

16.

Give a decimal approximation of your answer to the second question using 3.14 to approximate π.