How many inches tall should the new box be in order to hold exactly the same volume as the original box?

Question

A rectangular box with a base 2 inches by 6 inches is 10 inches tall and holds
12 ounces of breakfast cereal. The manufacturer wants to use a new box with a base
3 inches by 5 inches. How many inches tall should the new box be in order to hold
exactly the same volume as the original box? (Note: The volume of a rectangular box
may be calculated by multiplying the area of the base by the height of the box.)
A. 8
B. 9
C. 10
D. 11
E. 12

Answer 1

V original box = 2*6*10 = 120 in.³

Holds 12 oz.


To hold the same amount, it needs the same volume:

120 = 3*5*h, where 3 * 5 is the new area of the base, and h is the height of the new box.

120 = 15h

Divide by 15:

120/15 = 15h/15

h = 8 inches tall A)