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.
The expression
(
10
2
)
(
10
2
)
(
10
2
)
10
3
represents the number of Box
3
boxes that fit inside Box
2
.



Which TWO expressions show the number of Box
3
boxes that fit inside Box
2
?



A.
10
(
2
)
(
3
)
÷
3

B.
10
(
2
+
3
)
÷
3

C.
10
(
2
)
(
3
)
−
3

D.
10
(
2
+
2
+
2
−
3
)

E.
10
(
2
)
(
2
)
(
2
)
−
3

Answer 1

Box 2 volume = (100 cm)^3 = (10^2)^3 = (10^2)(10^2)(10^2).
Box 3 volume = 10^3.

Number that fit = (10^2)(10^2)(10^2) ÷ 10^3 = 10^(2+2+2−3).

That is written by choice D (10^(2+2+2−3)). It is also written by E as (10^2)(10^2)(10^2)·10^(−3), i.e. 10(2)(2)(2)−3.

Answer: D and E.