Question

MEDAL The volume of a cube is eighty-one cubic meters. What is the volume of the square based pyramid with the same side length and height?

nine cubic meters

twenty-seven cubic meters

two hundred forty-three cubic meters

seven hundred twenty-nine cubic meters

Answer 1

27 cubic meters.

Answer 2

length of the cube would be \[\sqrt[3]{81}\], then since the same length is brought over to the square based pyramid, (equation of square based pyramid =
(base edge)^2
times
(height/3),
just sub in \[\sqrt[3]{81}\] into the base edge and height (Ans^2)(Ans/3) = 27