A cube measures n inches on each edge. If a slice 5 inches thick is cut from one face of the cube, the resulting solid has a volume of 2250 cubic inches. Find n .
A)16 inches
B)12 inches
C)15 inches
D)8 inches
E)14 inches

Question

Quizplus · Accepted Answer

Let's first find the original volume of the cube before the slice is taken.
Original Volume = n^3
After the slice is taken, the new volume becomes:
New Volume = (n-5)^2 * 5
Given that the new volume is 2250 cubic inches:
(n-5)^2 * 5 = 2250
(n-5)^2 = 450
n-5 = 15 (since 15^2 = 225)
n = 20
Therefore, the original cube measures 20 inches on each edge. However, we need to subtract the slice of 5 inches from one face, so the final answer is:
n = 20 - 5 = 15 inches.

A Cube Measures N Inches on Each Edge