Question

A pyramid with a square base has a volume of 120 cubic meters and a height of 10 meters. what is a side length of the base?

Answer 1

`V=120\\ h=10\\ a=?\\\\ V=(1)/(3)a^2h\\ 120=(1)/(3)a^2\cdot10\\ a^2=36\\ a=6`

Answer 2

volume of a pyramid = length x width x height
3

because a square has the same length and width, length = width = side

volume of a pyramid = side x side x height
3

volume of a pyramid = side² x height
3

We know the volume of the pyramid is 120 cubic meters, and the height is 10 meters, so:

120 = side² x 10
3

multiply both sides by 3

360 = side² x 10

divide both sides by 10

36 = side²

square root both sides

6 = side

A side length of the base is 6 meters.