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6-8 Grade 8 Unit 5 Lesson 13

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Lesson 13

13.1 Warm-up 13.2 Activity 13.3 Activity 13.4 Activity Student Lesson Summary

Unit 5, Lesson 13

The Volume of a Cylinder

Grade 8

13.1

Warm-up

A Circle's Dimensions

Here is a circle. Points , , , and and segments and are drawn.

A circle with center A. Points C, D, and B are on the circle. Segment C B contains A. Segment D A, has length 4.

What is the area of the circle, in square units? Select all that apply.
5. approximately 25
6. approximately 50
If the area of a circle is square units, what is its radius? Explain your reasoning.

Are You Ready for More?

13.2

Activity

Circular Volumes

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

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

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

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

C

Are You Ready for More?

13.3

Activity

A Cylinder's Dimensions

For cylinders A–D, sketch a radius and the height. Label the radius with an and the height with an .
Earlier you learned how to sketch a cylinder. Sketch cylinders for E and F, and label each one’s radius and height.

Are You Ready for More?

13.4

Activity

A Cylinder's Volume

Here is a cylinder with height 4 units and diameter 10 units.
1. Shade the cylinder’s base.
2. What is the area of the cylinder’s base? Express your answer in terms of .
3. What is the volume of this cylinder? Express your answer in terms of .
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 30 feet and diameter of 12 feet. Make a sketch of this silo, and label its height and radius. How much volume, in cubic feet, does this silo hold? Use 3.14 as an approximation for .

Are You Ready for More?

Student Lesson Summary

We can find the volume of a cylinder with radius and height using two ideas we've seen before:

The volume of a rectangular prism is the result of multiplying the area of its base by its height.
The base of the cylinder is a circle with radius , so the base area is .

Remember that is the number we get when we divide the circumference of any circle by its diameter. The value of is approximately 3.14.

Just like a rectangular prism, the volume of a cylinder is the area of the base times the height. For example, consider a cylinder whose radius is 2 cm and whose height is 5 cm.

The base has an area of cm² (since ), so the volume is cm³ (since ). Using 3.14 as an approximation for , we can say that the volume of the cylinder is approximately 62.8 cm³.

A drawing of a cylinder whose radius is 2 and height is 5.

In general, the base of a cylinder with radius units has area square units. If the height is units, then the volume in cubic units is

Glossary

None