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?

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.

\( V=120\\ h=10\\ a=?\\\\ V=\dfrac{1}{3}a^2h\\ 120=\dfrac{1}{3}a^2\cdot10\\ a^2=36\\ a=6 \)


RELATED: