Volume of Cones and Pyramids

This video tutorial explains how to find the volumes of cones and pyramids using a common formula: one-third times the base area times the vertical height. The video details how to calculate the base area for different shapes, such as circles for cones and squares or triangles for pyramids. It provides example calculations for both cones and pyramids, demonstrating the application of the formula. The tutorial concludes with a prompt for viewers to practice with questions on the platform.

What is the common formula used to calculate the volume of both cones and pyramids?

• Base area times height

• One-third times base area times height

• Pi times radius squared times height

• Length times width times height

For a cone, how do you calculate the base area?

• One-third times base area

• Base times height divided by two

• Pi times radius squared

• Length times width

What is the formula for the volume of a cone?

• One-third times pi times radius squared times height

• Pi times radius squared times height

• Base area times height

• One-third times base area

How do you calculate the base area of a square-based pyramid?

• Base times height divided by two

• Pi times radius squared

• Length times width

• Length squared

If a pyramid has a triangular base, which formula is used to find the base area?

• Base times height divided by two

• Length squared

• Length times width

• Pi times radius squared

In the example given, what is the radius of the cone used to calculate its volume?

• 6 cm

• 4 cm

• 3 cm

• 5 cm

What is the vertical height of the cone in the example?

• 6 cm

• 12 cm

• 8 cm

• 10 cm

What is the volume of the cone calculated in the example?

• 256 cm³

• 200/3 pi cm³

• 160/3 pi cm³

• 100 pi cm³

In the pyramid example, what is the length of the base?

• 6 cm

• 10 cm

• 8 cm

• 12 cm

What is the calculated volume of the square-based pyramid in the example?

• 256 cm³

• 300 cm³

• 160 cm³

• 200 cm³