The volume of a rectangular solid varies jointly with its length, width, and height. If the length is tripled, the width is tripled, and the height is quadrupled, by what factor is the volume multiplied?
A) 3
B) 23
C) 9
D) 36

Question

Quizplus · Accepted Answer

Let V be the original volume, and let L, W, and H be the original length, width, and height, respectively. We know that V is jointly proportional to L, W, and H, so we can write:
V = kLWH
where k is some constant of variation.

If we triple the length, width, and height, we get a new volume, call it V', given by:
V' = k(3L)(3W)(4H) = 36kLWH

So the new volume is 36 times the original volume, which means the volume is multiplied by a factor of 36. Therefore, the answer is D, 36.

The Volume of a Rectangular Solid Varies Jointly with Its