Question

A jewelry box is designed such that its length is twice its width and its depth is 2 inches less than its width the volume of the box is 64 inches

What is the equation o f the volume of the box

Answer 1

`Volume = 2x^(3)-4x^(2)`

Explanation:

Let x be the width of the jewellery box

Given:

Length of the box is twice its width

Length of the box =
`2* width`

Length of the box =
`2* x= 2x`

depth of the box is equal to 2 inches less than its width.

depth of the box =
`width-2`

depth of the box =
`x-2`

The volume of the box is 64 inches.

Solution:

We know that the formula of the volume is.

`Volume = length* width* depth`

Now we substitute all known value in above.

`Volume = 2x* x* (x-2)`

`Volume = 2x^(2)(x-2)`

`Volume = 2x^(3)-4x^(2)`

Therefore, the equation of the volume of the box is.

`Volume = 2x^(3)-4x^(2)`