Question

A room has a total interior volume of
512
cubic meters. Inside the room are three cube-shaped boxes of different sizes.

Box
1
has a volume of
(
10
−
2
)
3
cubic kilometers.
Box
2
has a side length of
100
centimeters. The area of one face for the box is
10
,
000
square centimeters.
Box
3
has a volume of
10
3
cubic centimeters.
A worker wants to find the side length,
x
, for the room containing the boxes.



Which equation and explanation can the worker use to find the side length?



A.
x
3
=
512
; divide both sides of the equation by
3
to solve

B.
x
2
=
512
; divide both sides of the equation by
2
to solve

C.
x
3
=
512
; apply the cube root to both sides of the equationto solve

D.
x
2
=
512
; apply the square root to both sides of the equation to solve

Answer 1

C. Because the room is a cube, its volume is x^3 = 512. Take the cube root of both sides to solve: x = ∛512 = 8 (meters).