The square pyramid shown has a volume of 576 cubic centimeters and a height of 27 centimeters. The figure is not drawn to scale.
What is the value of s, the edge length of the base of the pyramid in centimeters?
To find the base edge length, we need to use the formula for the volume of a square pyramid:
Volume = (1/3) * base area * height
Given that the volume is 576 cubic centimeters and the height is 27 centimeters, we can rearrange the formula to solve for the base area:
576 = (1/3) * base area * 27
576 = 9 * base area
base area = 576 / 9
base area = 64
Since the base of a square pyramid is a square, the area of the base is s^2, where s is the length of the edge. Therefore:
s^2 = 64
s = √64
s = 8
Therefore, the edge length of the base of the pyramid is 8 centimeters.