Question

Paul has three​ cube-shaped boxes. Each box is a different size and they are stacked from the largest to the smallest. Some information about the boxes is given below. Answer questions 15 below.

The combined volume of the three boxes is​ 1,197 cubic inches.

The area of one face of the medium box is 49 square inches.

The volume of the smallest box is 218 cubic inches less than the volume of the medium box.

1. What is the volume of the medium​ box? Explain.

The edge length of the medium box is

â–Ľ

StartFraction StartRoot 49 EndRoot Over 2 EndFraction comma

StartRoot 49 EndRoot comma

RootIndex 3 StartRoot 49 EndRoot comma

StartFraction 49 Over 2 EndFraction comma

which equals

nothing. The volume of the box is the edge length

â–Ľ

squared,

doubled,

tripled,

cubed,

which equals

nothing

â–Ľ

cubic inch(es).

inch(es).

square inch(es).

Answer 1

Medium box: 343 in^3

Large box: 636 in^3

Explanation:

- Volume small box = 218 in^3

- Area face medium box = 49 in^2. (7x7=49)

Volume medium box = 7^3 = 343 in3

- Combine volume of the 3 boxes = 1,197 in^3

- Volume large box = 1,197 - 218 - 343 = 636 in^3