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