Digits, Grade 8, Volume 1, Homework Helper

5-5: Volumes of Spheres

Key Concept

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

You can find the formula for the volume of a sphere by comparing it with the volume of a cylinder with a height and diameter equal to the diameter of the sphere.

A cylinder with height and diameter 2r. A sphere with diameter 2r.

Fill the cylinder with water up to the 1 third mark.

Drop the sphere in the cylinder. When the sphere is completely submerged, the water level reaches the top of the cylinder.

In this cylinder, the height is equal to 2r.

Use the formula V = πr 2 h to find the volume of the cylinder.

The formula for the volume of this cylinder is V = 2πr 3.

The sphere filled two-thirds of the space in the cylinder.

table with 3 rows and 2 columns , row1 column 1 , cap volumeofthesphere , column 2 equals , 2 thirds , open . cap volumeofthecylinder . close , row2 column 1 , , column 2 equals , 2 thirds , open 2 pi , r super 3 end super , close , row3 column 1 , , column 2 equals , 4 thirds , pi r , end table


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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