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 10 square inches and a height of 9 inches?
The volume of the pyramid is blank cubic inches.
To solve this problem, we can set up a proportion based on the given information:
Volume1 / Base area1 x Height1 = Volume2 / Base area2 x Height2
Plugging in the values given:
24 / 24 x 3 = Volume2 / 10 x 9
Solving for Volume2:
24 / 72 = Volume2 / 90
Volume2 = (24/72) x 90
Volume2 = 30 cubic inches
Therefore, the volume of the pyramid with a base area of 10 square inches and a height of 9 inches is 30 cubic inches.