the base of a rectangular prism is congruent to the base of a pyramid. The height of the pyramid is 3 times the height of the prism. Which figure has a greater volume? Explain.

Question

I'm terrible with these kind of word problems. If you could explain that would be great.

Answer 1

The volume of the rectangular prism
= base area x height

the volume of the pyramid
= (1/3) base x height

If the height of the pyramid is 3 times the height

the factor of 3 would cancel the 1/3 of the formula, and their volumes would be equal.

Answer 2

wai the height of the pyramid is 3 times the height?
Can you just show how you got it with numbers like how you would on a piece of paper. Thanks!

Answer 3

let height of prism be h
let height of pyramid be 3 h, (they said so.)

volume of prism = (base)(h)

volume of pyramid = (1/3)(base)(3h)
= (base)(h)

They are the same !

Answer 4

ooohhhhh! I get it now! thanks so much!