Volume of Cones and Cylinders

This video tutorial covers how to find the volume of a cone using the formula 1/3 × π × radius² × height. It begins with a review of the volume of a cylinder and explains how the volume of a cone is 1/3 that of a cylinder with the same base and height. The tutorial includes examples of calculating the volume of cones with given dimensions and solving for missing dimensions using the formula.

What is the formula for the volume of a cylinder?

• Volume = pi * radius * height

• Volume = pi * radius^2 * height

• Volume = 2 * pi * radius * height

• Volume = pi * radius^2

How does the volume of a cone compare to a cylinder with the same base and height?

• The cone's volume is one-third that of the cylinder.

• The cone's volume is half that of the cylinder.

• The cone's volume is twice that of the cylinder.

• The cone's volume is the same as the cylinder.

If a cone has a diameter of 15 cm, what is its radius?

• 5 cm

• 30 cm

• 7.5 cm

• 15 cm

What is the volume of a cone with a radius of 2 feet and a height of 3 feet?

• 18.84 cubic feet

• 25.12 cubic feet

• 12.56 cubic feet

• 6.28 cubic feet

How do you calculate the volume of a cone with a diameter of 6 cm and a height of 11.5 cm?

• pi * 6^2 * 11.5

• pi * 3^2 * 11.5

• 1/3 * pi * 6^2 * 11.5

• 1/3 * pi * 3^2 * 11.5

What is the first step in finding a missing radius when given the volume and height of a cone?

• Divide the volume by the height.

• Divide the volume by 1/3 and pi.

• Multiply the volume by the height.

• Multiply 1/3, pi, and the height.

If the volume of a cone is 100.48 cubic inches and the height is 6 inches, what is the radius?

• 6 inches

• 4 inches

• 2 inches

• 8 inches

What is the final step in solving for the radius when given the volume and height of a cone?

• Take the square root of both sides.

• Divide both sides by the height.

• Multiply both sides by pi.

• Multiply both sides by the height.

What is the relationship between the volume of a cone and a cylinder with the same dimensions?

• The cone's volume is one-third the cylinder's volume.

• The cone's volume is half the cylinder's volume.

• The cone's volume is twice the cylinder's volume.

• The cone's volume is equal to the cylinder's volume.

What is the formula for the volume of a cone?

• Volume = pi * radius^2 * height

• Volume = 1/3 * pi * radius^2 * height

• Volume = 2/3 * pi * radius^2 * height

• Volume = pi * radius * height