Digits, Grade 8, Volume 1, Homework Helper

5-3: Volumes of Cylinders

Key Concept

Volume of a Cylinder

The volume of a cylinder is the number of unit cubes, or cubic units, needed to fill the cylinder.

If each layer is one unit high, then the height h represents the number of layers.

The area of the circular base is represented by pr2h.

The formula for the volume of a cylinder is the area of the base times the height.

The volume of a cylinder is represented by πr 2 h.

Part 1

Example Finding Volumes of Cylinders

What is the volume of each cylinder in terms of π?

  • a. A cylinder with height 6 cm and radius 4 cm.

  • b. A cylinder with height 5 cm and radius 5 cm.

  • c. A cylinder with height 4 cm and radius 6 cm.

Solution

  • a. table with 3 rows and 2 columns , row1 column 1 , v , column 2 equals pi , r squared , h , row2 column 1 , , column 2 equals pi . open 4 close squared . open 6 close , row3 column 1 , , column 2 equals 96 pi , end table

    The volume of the cylinder is 96π cm3.

  • b. table with 3 rows and 2 columns , row1 column 1 , v , column 2 equals pi , r squared , h , row2 column 1 , , column 2 equals pi . open 5 close squared . open 5 close , row3 column 1 , , column 2 equals 125 pi , end table

    The volume of the cylinder is 125π cm3.

  • c. table with 3 rows and 2 columns , row1 column 1 , v , column 2 equals pi , r squared , h , row2 column 1 , , column 2 equals pi . open 6 close squared . open 4 close , row3 column 1 , , column 2 equals 144 pi , end table

    The volume of the cylinder is 144π cm3.


End ofPage 172

Table of Contents

Digits, Grade 8, Volume 1, Homework Helper Unit A: Number and Operations Unit B: Proportionality Unit C: Expressions, Equations, and Relationships English/Spanish Glossary Formulas Math Symbols Formulas Measures Properties