In a regular quadrangular pyramid, the height is 12 cm, and the apothem is 45 cm. Find the volume of the pyramid.

In order to solve this problem, you need to represent the situation graphically and know the formula for the volume of the pyramid. Let the length of the edge of the base be a. Then, the height divides it in half, then this half will be (a / 2). a / 2 = √ (45 ^ 2 – 12 ^ 2) = 3√209. a = 6√209.

V = 1/3 * Sbn * h = a ^ 2 * h / 3 = 36 * 209 * 12/3 = 30096 cm3.

Therefore, our answer is 30,096 cm3.