1. Lesson 4.8
Core Focus on Geometry
Volume of Spheres

2. Warm-Up 1. 2. 3. 4. The area of a circle is about 200.96 cm2.
4. The area of a circle is about cm2.
Determine the length of the radius. 6 9 12
8 cm 3 8 2

3. Lesson 4.8
Volume of Spheres
Find the volume of spheres and solve real-world problems involving spheres.

4. Vocabulary Sphere A round, curved, closed three-dimensional solid.
Good to know!
 A sphere has no edges, sides or vertices.
 All the points on the surface of a sphere are exactly the same distance from the center of the sphere. This distance is called the radius of the sphere.
 If something is “spherical,” that means it is shaped like a sphere.
“sf-ear-i-cull”

5. Volume of a Sphere
The volume (V ) of a sphere is equal to four-thirds of the product of pi (π) and the cube of the radius (r3).
Center
radius

6. Example 1
Find the volume of the sphere. Use 3.14 for π. Use the formula for a sphere. Substitute known values for the variables. Find the value of the power. Multiply. The volume of the sphere is about cm3.

7. Example 2
A water tower has a spherical tank. The diameter of the tank is 30 meters. How much water can the tank hold? Use 3.14 for π. Find the length of the radius. Diameter ÷ 2 = 30 ÷ 2 = 15 Write the volume formula for a sphere. Substitute known values for the variables. Find the value of the power. Multiply. The tank can hold approximately 14,130 cubic meters of water.

8. Example 3
A bouncy ball has a volume of cubic centimeters. Find the radius of the ball. Use 3.14 for π. Write the formula for a sphere. Substitute known values for the variables. Multiply. Divide both sides of the equation by Cube root both sides of the equation. The radius of the bouncy ball is 3 cm.
This is a rounded answer. Rounding can make cubic roots easier to calculate.

9. Communication Prompt
Why are volumes that use 3.14 for  approximations? How could a solution that uses pi be more exact?

10. Exit Problems 1. Find the volume of the sphere. Use 3.14 for .
2. Find the length of the radius of a sphere with a volume of about cubic inches. Use 3.14 for .
3.5 m
≈ cubic meters
4 inches