Question

A square pyramid and a rectangular pyramid have the same height. The base area of the square pyramid is half the base are of the rectangular pyramid. Compare their volumes.

I think that the volume of the square pyramid is 1/2 the volume of the rectangular pyramid because 2 squares make a rectangle. Am I right? Thank you!

Answer 1

Your answer is correct, but your reasoning isn't exactly correct.

The volume of the square pyramid is 1/2 the volume of the rectangular pyramid because the base area of the square is 1/2 of the base area of the rectangle.

As per the formula V = (1/3)*h*A, you can obtain the above answer.

However, this does not necessarily mean that '2 squares of the base will make the rectangle'.

Let me give an example,

Imagine the square base has side 2 (and hence area 4), and the rectangle has lengths 1 and 8 (hence area 8). The area of the square is 1/2 times that of the rectangle but two of the squares in this case do not make the rectangle together.

Answer 2

good explanation.