Unit 5, Lesson 13
The Volume of a Cylinder
Grade 8
13.1
Warm-up
Here is a circle. Points , , , and and segments and are drawn.
- What is the area of the circle, in square units? Select all that apply.
- approximately 25
- approximately 50
- If the area of a circle is square units, what is its radius? Explain your reasoning.
13.2
Activity
What is the volume, in cubic units, of each figure? Even if you aren’t sure, make a reasonable guess.
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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
13.3
Activity
-
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.
13.4
Activity
-
Here is a cylinder with height 4 units and diameter 10 units.
-
Shade the cylinder’s base.
- What is the area of the cylinder’s base? Express your answer in terms of .
- 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 .
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.
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
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