Sphere Volume and Properties

This lesson in module 13 covers how to find the volume of spheres and hemispheres. It begins with an introduction to the formula for the volume of a sphere, V = 4/3 πr³, and explains the concept of radius. The lesson includes examples such as calculating the volume of a basketball and a baseball, finding the radius from a given volume, and determining the volume of a hemisphere. The lesson emphasizes the importance of using exact values and rounding only at the end of calculations.

What is the formula for the volume of a sphere?

• V = 4/3 π r^2

• V = 4/3 π r^3

• V = 2/3 π r^3

• V = π r^3

What is the definition of a sphere?

• A two-dimensional figure with varying distances from the center

• A three-dimensional figure with varying distances from the center

• A three-dimensional figure with all points the same distance from the center

• A two-dimensional figure with all points the same distance from the center

In the first example, what is the radius of the basketball used to calculate the volume?

• 16 cm

• 10 cm

• 12 cm

• 14 cm

How do you calculate the volume of a sphere if you are given the diameter?

• Use the diameter directly in the formula

• Divide the diameter by 2 to find the radius, then use the formula

• Multiply the diameter by π

• Square the diameter and multiply by 4/3 π

What is the approximate volume of a baseball with a diameter of 3 inches?

• 14.1 inches cubed

• 16.2 inches cubed

• 18.3 inches cubed

• 12.5 inches cubed

When given the volume of a sphere, what is the first step to find the radius?

• Subtract π from the volume

• Divide the volume by π

• Cube root the volume

• Multiply the volume by 4/3

What is the radius of a sphere with a volume of 562.5 π feet cubed?

• 9.5 feet

• 6.5 feet

• 8.5 feet

• 7.5 feet

How is the volume formula for a hemisphere different from that of a full sphere?

• It is multiplied by 1/3

• It is multiplied by 1/2

• It is multiplied by 3/4

• It is multiplied by 2/3

What is the exact volume of a hemisphere with a radius of 6 meters?

• 72 π meters cubed

• 108 π meters cubed

• 144 π meters cubed

• 216 π meters cubed

What is the approximate volume of a hemisphere with a radius of 6 meters?

• 452.4 cubic meters

• 500.2 cubic meters

• 700.5 cubic meters

• 600.3 cubic meters