Question

When the dimensions of a cube are reduced by 4 inches on each side, the surface area of the new cube is 864 square inches. What where the dimensions of the original cube?

Answer 1

Answer:

The dimensions of the original cube are 16 in x 16 in x 16 in

Step-by-step explanation:

Let

x ----> the length side of the original cube

The surface area of the cube is equal to

$SA=6b^2$

where

b is the length side of the cube

we know that

The dimensions of a cube are reduced by 4 inches on each side and the surface area of the new cube is 864 square inches

so

The length side of the new cube is

$b=(x-4)\ in$

substitute in the formula of surface area

$SA=6(x-4)^2$

$SA=864\ in^2$

so

$6(x-4)^2=864$

Simplify

$(x-4)^2=144$

take square root both sides

$(x-4)=(+/-)12$

$x=4(+/-)12$

$x=4(+)12=16\ in$

$x=4(-)12=-8\ in$ ----> the length side cannot be a negative number

therefore

The dimensions of the original cube are 16 in x 16 in x 16 in