Lesson 4.8 Core Focus on Geometry Volume of Spheres

Warm-Up 1. 2. 3. 4. The area of a circle is about 200.96 cm2. 1. 2. 3. 4. The area of a circle is about 200.96 cm2. Determine the length of the radius. 5. 6. 7. 6 9 12 8 cm 3 8 2

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

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”

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

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 523.33 cm3.

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.

Example 3 A bouncy ball has a volume of 113.04 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 4.19. 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.

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

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 267.95 cubic inches. Use 3.14 for . 3.5 m ≈ 179.5 cubic meters 4 inches