Volume and Area of Cones and Pyramids

This video tutorial explains how to calculate the volume of cones and pyramids using the formula: one-third of the base area times the height. It demonstrates the process with examples, starting with a cone, where the base is a circle, and then a pyramid, where the base is a square. The tutorial also covers using the Pythagorean theorem to find the height when given the slant height. The video emphasizes the similarity between the volume formulas for cones, pyramids, and prisms, highlighting the division by three for cones and pyramids.

What is the formula for finding the volume of a cone or pyramid?

• Base area times height

• One-third of base area plus height

• One-third of base area times height

• Base area plus height

What shape is the base of a cone?

• Rectangle

• Circle

• Triangle

• Square

How do you find the height of a cone if you have the slant height?

• Divide the slant height by the radius

• Use the Pythagorean theorem

• Use the area formula

• Multiply the slant height by two

What is the base area of a cone with a radius of 5?

• 100π

• 50π

• 25π

• 5π

What is the volume of a cone with a base area of 25π and height of 12?

• 150π

• 200π

• 100π

• 300π

What is the shape of the base of the pyramid discussed in the video?

• Rectangle

• Square

• Triangle

• Circle

If the side of a square base is 10, what is the base area?

• 100

• 150

• 50

• 200

What is the height of the pyramid if the slant height is 13 and half the base is 5?

• 12

• 11

• 10

• 13

How do you calculate the volume of a pyramid?

• Base area times height

• One-third of base area times height

• Base area plus height

• One-third of base area plus height

What is the volume of a pyramid with a base area of 100 and height of 12?

• 600

• 500

• 400

• 300