The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is 24 cubic inches when its base area is 24 square inches and its height is 3 inches. What is the volume of a pyramid with a base area of 15 square inches and a height of 7 inches?
The volume of the pyramid is __ cubic inches.
We can set up a proportion to solve this problem. Let the volume of the pyramid be V, the base area be B, and the height be H. We are told that V varies jointly with B and H, so we can write V = k * B * H, where k is the constant of variation.
We are given that when B = 24 square inches and H = 3 inches, V = 24 cubic inches. Plugging these values into the equation, we get 24 = k * 24 * 3.
Simplifying the equation, we have 24 = 72k. Dividing both sides by 72, we find k = 24/72 = 1/3.
Now we can use this value of k to find the volume of a pyramid with B = 15 square inches and H = 7 inches. Plugging these values into the equation, we get V = (1/3) * 15 * 7.
Simplifying the expression, we find V = 105/3 = 35 cubic inches.
Therefore, the volume of the pyramid is 35 cubic inches.