please prove the formula for volume of a pyramide?

Answer 1

A pyramid can be expressed by the following:

A(z) = Ab [(z-h)^2/h^2]

Where Ab is the area of the base of some arbitrary pyramid.
At the base, z = 0 and at the peak, z = h.

So the volume is therefore given by:

int(from 0 to h) of A(z) dz where int stands for integral. Which is the same thing as:

int(from 0 to h) of Ab[(z-h)^2/h^2] dz, take out the h^2 in the denominator (since it is a constant) to get:

Ab/h^2 int(from 0 to h) of [(z-h)^2] dz

Now expand (z-h)^2 to get:

Ab/h^2 int(from 0 to h) of [z^2 - 2hz + h^2] dz

Take the integral and sub in the value for h to get:

Ab/h^2 [(1/3)h^3 - h^3 + h^3]

The -h^3 + h^3 cancels out and leaves you with:

Ab/h^2[(1/3)h^3]...the h^2 cancels with h^3 to leave you with:

(1/3)(Ab)(h).

Which is area of the base multiplied by the height divided by 3.

Answer 2

Volume = Area of the base * height / 3

₢

Answer 3

volume=Base x hight x 3

Answer 4

EASY YOU SEE. x+y+ 4 { CSQ <7>5 '' " AT 10 o "2 = 6.7<2.2 +Y WHEN R IN 3>5 _ =Y 4

Answer 5

u should ask this question to albert einstein..