This pyramid has the same base as the prism, and its height is three times the height of the prism. What is the ratio of the volume of the pyramid to the volume of the prism? A. ' ("volume of pyramid") / ("volume of prism") = 1' B. ' ("volume of pyramid") / ("volume of prism") = 1/9' C. ' ("volume of pyramid") / ("volume of prism") = 3' D. ' ("volume of pyramid") / ("volume of prism") = 2/3'

Option A is the correct answer.

Explanation:

Let A be the base area and h be the height of prism.

Volume of prism = Base area x Height = a x h = ah

Now we have base area of pyramid = Base area of prism = a (both have same type of base)

Height of pyramid = 3 x height of prism = 3h

Volume of pyramid = 1/3 x Base area x Height = 1/3 x a x 3h = ah

Comparing both volumes, we will get Volume of prism = Volume of pyramid

So their ratio is 1.

Option A is the correct answer.