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Oct 01, 2024

Question

easy

The volume of a pyramid varies directly jointly with its height and the area of its base. A pyramid with a height of 12 feet and a base with an area of 23 square feet has a volume of 92 cubic feet. Find the volume, in cubic feet, of a pyramid with a height of 13 feet and a base with an area of 24 square feet.

48

104

192

276

312

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Scott Woodbury-Stewart Founder and Expert GMAT Instructor

Solution:

We can let V, h, and A represent the volume, height, and base area of the pyramid, respectively. Because V varies directly jointly with h and A, we can set up a joint variation equation V=khA , where k is some unknown constant. Substituting the initial given values for V, h, and A, we can solve for k.

V=khA 92=k(12)(23) 92 276 =k 1 3 =k

Now that we know the value of k in a pyramid’s volume equation, we can determine V when h = 13 and A = 24.

V= 1 3 hA V= 1 3 (13)(24) V=104

The volume of the pyramid is 104 cubic feet.

Correct answer: B

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