Question

Cooper’s Storage and Shipping Company is working with a local business to package some office supplies. The supplies are packed inside a cube – shaped box with side lengths 4 ½ in. These boxes are then packed into a shipping box with dimensions of 18 in x 9 in x 4 ½ in. What is the volume of the cube – shaped box? Show your work. What is the volume of the shipping box? Show your work. How many boxes of office supplies can be packed into the larger box for shipping? Show your work.

Answer 1

8

Explanation:

4 1/2=9/2*9/2=81/4*9/2=729/8

9/1*9/2*18/1=1,458/2

1,458/2*8/729=11,664/1,458

=8

So eight boxs of office supplies can be packed.

Answer 2

1. Volume of cube-shaped box = 91.125 cubic inches

2. Volume of shipping box = 729 cubic inches

3. 8 boxes of office supplies can be packed into the larger box for shipping.

Explanation:

1.

The first question asks for the volume of a cube. The formula is V = s^3, where, s is the side length and V is the volume. Thus plugging in, we get:

`V=s^3\\V=(4(1)/(2))^3\\V=(4.5)^3\\V=91.125`

Volume of cube-shaped box = 91.125 cubic inches

2.

The second question asks for the volume of the shipping box. Since 3 measurements are given, the shipping box is a rectangular prism. The volume of a rectangular prism is V = l * w * h, where

V is the volume

l is the length

w is the width, and

h is the height

Plugging in all the info we know (multiplying the 3 numbers - dimensions), we can get the volume of the shipping box. So:

`V=lwh\\V=(18)(9)(4(1)/(2))\\V=(18)(9)(4.5)\\V=729`

Volume of shipping box = 729 cubic inches

3.

Since the volume of a single box of office supplies (cub-shape) is 91.125 cu. in., and the volume of larger shipping box is 729, we can divide 729 by 91.125 to find how many of them would fit the large box.

`(729)/(91.125)=8`

Hence, 8 boxes of office supplies can be packed into the larger box for shipping.