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6-8 Accelerated 7 Unit 6 Lesson 11

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K-5 Math •6-8 Math 9-12 Math

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Accelerated 6 •Accelerated 7

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Unit 1 Unit 2 Unit 3 Unit 4 Unit 5 •Unit 6 Unit 7 Unit 8 Unit 9

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Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 •Lesson 11 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22 Lesson 23

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Lesson 11

11.1 Warm-up 11.2 Activity 11.3 Activity 11.4 Activity Student Lesson Summary

Unit 6, Lesson 11

The Volume of a Cylinder

Accelerated 7

11.1

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.

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11.2

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

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11.3

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.

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11.4

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 .

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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

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