The Volume of a Pyramid

Question

The volume of pyramid varies jointly as its height and the area of its base. A pyramid with the height of 12 feet and base with area is 23 square feet has a volume of square area of 92 cubic feet. Find the volume of a pyramid with a height of 17 feet and a base with an area of 27 square feet.

Answer 1

"varies jointly" means V = k*H*B where k is a constant to be determined, H is the height and B is the area of the base

 

92 = k * 12 * 23 => k = 1/3

 

Therefore V = (1/3) * 17 * 27 = 153