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Volume of a Rectangular Pyramid. The height of the pyramid and the prism are the same. Consider the prism and pyramid. The base of the pyramid and the prism are the same.

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volume of a rectangular pyramid
Volume of a Rectangular Pyramid

The height of the pyramid and the prism are the same

  • Consider the prism and pyramid

The base of the pyramid and the prism are the same

If you filled the pyramid with water and emptied it into the prism, how many times would you have to fill the pyramid to completely fill the prism to the top ?

This shows that the prism has three times the volume of a pyramid with the same height and length. Or the pyramid is 1/3 of the prism

slide2

5 in

The experiment on the previous slide allows us to work out the formula for the volume of a pyramid:

The formula for the volume of a prism is :

V = lwh

We have seen that the volume of a prism is three times more than that of a pyramid with the same diameter and height .

The formula for the volume of a pyramid is:

4 in

4 in

slide3

10 in

8 in

6 in

10 in

7 in

3 in

volume of a cone

D

D

H

H

Volume Of A Cone.

Consider the cylinder and cone shown below:

The diameter (D) of the top of the cone and the cylinder are equal.

The height (H) of the cone and the cylinder are equal.

If you filled the cone with water and emptied it into the cylinder, how many times would you have to fill the cone to completely fill the cylinder to the top ?

This shows that the cylinder has three times the volume of a cone with the same height and radius.

3 times.

slide5

r

h

r = radius h = height

The experiment on the previous slide allows us to work out the formula for the volume of a cone:

The formula for the volume of a cylinder is :

V =  r 2 h

We have seen that the volume of a cylinder is three times more than that of a cone with the same diameter and height .

The formula for the volume of a cone is:

slide6

(2)

(1)

18m

13m

6m

9m

Calculate the volume of the cones below:

slide7

(3)

8m

10m

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