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### Course: High school geometry>Unit 9

Lesson 2: Cavalieri's principle and dissection methods

# Volumes of cones intuition

Use Cavalieri's Principle to establish that the formula for the volume of a cone is the same as the formula for the volume of a pyramid (1/3 * base area * height). Created by Sal Khan.

## Want to join the conversation?

• If I look at the two pictures, did Sal consider the correct "h" in the left picture, because "h" is not perpendicular to the base, whilst in the right picture "h" is perpendicular to the base?! In other words should Sal have drawn a perpendicular from the top onto the base of the left picture as "h"? I hope to receive a reply...thanks very much, gui

p.s. One last remark I would like to make is that the way Sal drew the pictures, they can't have the same volume, because in the left picture "h" is not the perpendicular height with respect to its base!
• The 2 pictures are not the same shape. One is a pyramid and the other is a cone. The formulas used to find their surface area are different which is why a different approach is being taken.

And, 2 different shapes can have the same area. A square that is 4 by 4 has area 16. A triangle with base 6.4 and height 5 also has area of 16.
• Others have asked this question, but I haven't seen an explanation that I understand. The height of a pyramid is measured from the vertex/apex to the center of the base--not the length of one edge, right? In this video, the diagram shows height as being the length of one vertical edge of the pyramid. Shouldn't the height of both the cone and the pyramid be measured using the same method: Distance from the center of the base to the vertex/apex? Thank you for your help!
• I have submitted a request in "Report a Problem." You are correct in that the height of a right pyramid should be measured from the base to the center of the base. We have to wait and see if anything happens, I will pass on any response, or one day you may see a correction box.
• What's the volume of a cone?
• The formula for the volume of a cone is pi*radius squared*(height of the cone/3)
• Why the height of pyramid is not 90 degree perpendicular ?please help I don’t understand how the height of a pyramid can be not perpendicular side.