A right square pyramid has a base with edges each measuring 3 cm and a height twice the perimeter of its base. What is the volume of the pyramid?
I know that the formula for the volume of a pyramid is one-third times the area of the base times the height. So I need to find the area of the base and the height of the pyramid. The base is a square with side length 3 cm, so its area is 3 times 3, or 9 cm^2. The height of the pyramid is twice the perimeter of the base, so I need to find the perimeter of the base. The perimeter of a square is four times the side length, so the perimeter of the base is 4 times 3, or 12 cm. That means the height of the pyramid is 2 times 12, or 24 cm. Now I have everything I need to plug into the formula for the volume. The volume is one-third times 9 cm^2 times 24 cm, or 72 cm^3. 