Question

A right pyramid is a 3-D figure. Suppose that the base of a right pyramid has a diagonal with a length of 46.67 centimeters. If the height of the pyramid is 24.93 centimeters, find the volume of the pyramid. Round the answer to the nearest tenth of a cubic centimeter.

Answer 1

Let the base of the pyramid be a square, then
s^2 + s^2 = 46.67^2
2s^2 = 2178.0889
s^2 = 2178.0889 / 2 = 1089.04445
s = 33

Volume = Area of the base x height
Area of the base = s^2 = 33^2 = 1089

Therefore, volume = 1089 x 24.93 = 27,148.77 cubic centimeter