The base of the pyramid is a square with a side of 5, and the volume is 100. Find the height of the pyramid.

Since, according to the condition of this problem, we know the volume of this pyramid and the length of the square that serves as its base, in order to find the height of the pyramid, we need to use the volume formula:

V = 1/3 * S * h, where:

V is the volume of the pyramid;

S is the area of its base;

h – height.

In order to find the area of the base of the pyramid, we use the formula for the area of a square:

S = a ^ 2;

S = 5 ^ 2 = 25 cm2.

In order to calculate the height of a given pyramid, you need to divide its volume by one third of its area:

h = V: S / 3 = 3V / S;

h = 3 * 100/25 = 300/25 = 12 cm.

Answer: the height of the pyramid is 12 cm.