The volume of a pyramid varies jointly with the base area of the pyramid and its height. The volume of one pyramid is 35 cubic inches when its base area is 15 square inches and its height is 7 inches. What is the volume of a pyramid with a base area of 36 square inches and a height of 5 inches?
The volume of the pyramid is blank cubic inches.
The solution is
First, we need to find the constant of variation (k) for the given pyramid.
Using the formula for the volume of a pyramid, V = (1/3) * base area * height, we can set up the following equation using the given values:
35 = (1/3) * 15 * 7 * k
35 = 35k
k = 1
Now that we have the constant of variation, we can find the volume of the second pyramid:
V = (1/3) * 36 * 5 * 1
V = 60 cubic inches
Therefore, the volume of a pyramid with a base area of 36 square inches and a height of 5 inches is 60 cubic inches.