Answer:
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.
Step-by-step 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:
[tex]V=s^3\\V=(4\frac{1}{2})^3\\V=(4.5)^3\\V=91.125[/tex]
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:
[tex]V=lwh\\V=(18)(9)(4\frac{1}{2})\\V=(18)(9)(4.5)\\V=729[/tex]
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.
[tex]\frac{729}{91.125}=8[/tex]
Hence, 8 boxes of office supplies can be packed into the larger box for shipping.
