Calculating Volumes of Pyramids and Cones

The video tutorial covers the calculation of volumes for pyramids and cones. It begins with an introduction to the concepts of height and volume, followed by the formula for finding the volume of a pyramid: V = 1/3 * B * H, where B is the area of the base and H is the height. The tutorial includes examples and exercises for students to practice calculating the volume of pyramids with square bases. It then transitions to cones, explaining that the volume formula is similar, using the area of a circular base. The video provides examples and exercises for calculating cone volumes, emphasizing the use of the circle area formula.

What is the formula for calculating the volume of a pyramid?

• V = 1/2 * B * H

• V = π * r^2 * H

• V = B * H

• V = 1/3 * B * H

How is the height of a pyramid or cone measured?

• From the base to the vertex along the slant

• From the vertex to the base along a line perpendicular to the base

• From the center of the base to the vertex

• From one edge of the base to the opposite edge

What does the 'B' in the volume formula V = 1/3 * B * H represent?

• The radius of the base

• The diameter of the base

• The area of the base

• The perimeter of the base

If a pyramid has a square base of side 5 feet and a height of 9 feet, what is its volume?

• 225 cubic feet

• 75 cubic feet

• 45 cubic feet

• 135 cubic feet

For a pyramid with a square base, if one side of the base is 6 cm and the height is 10 cm, what is the volume?

• 120 cm^3

• 360 cm^3

• 72 cm^3

• 180 cm^3

If the area of the base of a pyramid is 36 square cm and the height is 10 cm, how do you calculate the volume?

• Divide the base area by the height

• Square the base area and multiply by the height

• Multiply the base area by the height and divide by 3

• Multiply the base area by the height

What is the formula to calculate the volume of a cone?

• V = 1/4 * π * r^2 * H

• V = π * r^2 * H

• V = 1/3 * π * r^2 * H

• V = 2/3 * π * r^2 * H

If a cone has a radius of 4 feet and a height of 6 feet, what is its volume?

• 32π cubic feet

• 96π cubic feet

• 64π cubic feet

• 48π cubic feet

What shape is the base of a cone?

• Triangle

• Circle

• Rectangle

• Square

For a cone with a radius of 3 meters and a height of 5 meters, what is the volume?

• 45π cubic meters

• 47.1 cubic meters

• 15π cubic meters

• 9π cubic meters