Question

Sam stores his coin collection in a cube-shaped box that has a volume of 27 in. He moves the coins into a larger cube-

shaped box that has a volume of 729 in. What is the difference in inches between the edge lengths of the two boxes?

Answer 1

Answer: 6 in.

Explanation:

Given

The volume of the small cube is
`V_1=27\ in.^3`

The volume of the large cube box is
`V_2=729\ in.^3`

The volume of a cube is
`(a)^3`

`\Rightarrow a_1^3=27\quad (a_1=\text{side length of small cube})\\\Rightarrow a_1=3\ in.\\\Rightarrow a_2^3=729\quad (a_2=\text{side length of large cube})\\\Rightarrow a_2=9\ in.`

The DIfference between the edge length is
`a_2-a_1=9-3=6\ in.`