Sam has two figures, one square pyramid and one rectangular prism. The pyramid has a height of 6 inches and a base length of 4 inches. The rectangular prism has a length of 8 inches, a width of 2 inches, and a height of h inches. If both figures have the same volume, what is the height of the rectangular prism?

Question

Eddie Acosta

Mathematics

19 December, 18:53

Sam has two figures, one square pyramid and one rectangular prism. The pyramid has a height of 6 inches and a base length of 4 inches. The rectangular prism has a length of 8 inches, a width of 2 inches, and a height of h inches. If both figures have the same volume, what is the height of the rectangular prism?

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Answers (1)

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Cale Fitzpatrick · Answer 1

1/2 inches

Step-by-step explanation:

Volume of a pyramid: (LWH) / 3

Volume of a rectangular prism: L*W*H

So if the volumes of both shapes are equal then

(lwh) / 3=lwh

Lets substitute the numbers give in the problem into the formula

6*4/3=8*2*h

24/3=16h

8=16h

Divide both sides by 16

8/16=h

1/2=h