Question

Ed decided to build a storage box. At first, he was planning to build a cubical box with edges of length n

inches. To increase the amount of storage, he decided to make the box 1 inch taller and 2 inches longer,
while keeping its depth at n inches. The volume of the box Ed built has a volume how many cubic inches
greater than the box he originally planned to build?
O 3n2 + 2n
312 + 3n+3
O 6n2 + 3n
O 6n2 + 3n+3

Answer 1

Given:

Edge of a cubic box = n inches.

He decided to make the box 1 inch taller and 2 inches longer, while keeping its depth at n inches.

To find:

How many cubic inches greater than the box he originally planned to build?

Solution:

Edge of a cubic box is n inches, so the volume of the original cube is:

`V_1=(edge)^3`

`V_1=n^3`

According to the given information,

New width of the box = n+1

New length of the box = n+2

New height of the box = n

So, the volume of the new box is:

`V_2=Length* width* h`

`V_2=(n+2)(n+1)n`

`V_2=(n^2+2n+n+2)n`

`V_2=(n^2+3n+2)n`

`V_2=n^3+3n^2+2n`

Now, the difference between new volume and original volume is:

`V_2-V_1=n^3+3n^2+2n-n^3`

`V_2-V_1=3n^2+2n`

So, the volume of new box is 3n^2+2n cubic inches more than the original box.

Therefore, the correct option is A.