Volume Calculations for Geometric Shapes

Mr. Richards teaches how to calculate the volume of pyramids, cones, and spheres. The lesson covers the formulas for each shape, including the volume of a pyramid as one-third the base area times height, the volume of a cone as one-third the base area (πr²) times height, and the volume of a sphere as four-thirds π times the radius cubed. The lesson includes examples and a practical application involving a beach ball to demonstrate the concepts.

If a pyramid has a base area of 225 square inches and a height of 12 inches, what is its volume?

• 300 cubic inches

• 2700 cubic inches

• 900 cubic inches

• 750 cubic inches

What is the formula for the volume of a pyramid?

• Area of the base times height

• Four-thirds pi times radius cubed

• One-third the area of the base times height

• Pi times radius squared times height

How is the volume of a cone calculated?

• Pi times radius squared times height

• One-third pi times radius squared times height

• One-third the area of the base times height

• Four-thirds pi times radius cubed

What is the volume of a cone with a radius of 5.5 meters and a height of 8 meters, rounded to the nearest tenth?

• 300.7 cubic meters

• 200.5 cubic meters

• 253.3 cubic meters

• 150.2 cubic meters

Which formula is used to calculate the volume of a sphere?

• Four-thirds pi times radius cubed

• One-third the area of the base times height

• Pi times radius squared times height

• Area of the base times height

What is the volume of a sphere with a radius of 5 feet, rounded to the nearest tenth?

• 450.2 cubic feet

• 600.5 cubic feet

• 500.0 cubic feet

• 523.3 cubic feet

A beach ball has a diameter of 12 inches. What is its radius?

• 10 inches

• 12 inches

• 6 inches

• 8 inches

What is the volume of a beach ball with a radius of 6 inches, rounded to the nearest tenth?

• 800.0 cubic inches

• 700.2 cubic inches

• 950.5 cubic inches

• 904.3 cubic inches

If a beach ball deflates at a rate of 1.5 cubic inches per minute, how long will it take to deflate completely?

• 800.2 minutes

• 602.9 minutes

• 500.0 minutes

• 700.5 minutes

How many hours approximately will it take for the beach ball to deflate completely?

• 12 hours

• 10 hours

• 15 hours

• 8 hours