The volume of a rectangular solid varies jointly with its length, width, and height. If the length is doubled, the width is tripled, and the height is quadrupled, by what factor is the volume multiplied?
A) 3
B) 12
C) 6
D) 24

Question

Quizplus · Accepted Answer

Let V be the original volume, and let L, W, and H be the original length, width, and height, respectively. Then we have:

V = kLWH

for some constant k. Now if the length is doubled, the width is tripled, and the height is quadrupled, we get a new volume V', given by:

V' = k(2L)(3W)(4H) = 24kLWH = 24V

So the new volume is 24 times the original volume, which means the volume is multiplied by a factor of 24. Therefore, the answer is D, 24.

The Volume of a Rectangular Solid Varies Jointly with Its