Question

Yasmin is wrapping a box in the shape of a cube with a side length of (2x-3)

A. What is the surface area of the box?

B. What is the volume of the box

Answer 1

Given:

Each side of the cube shaped box =
`2x-3`

To find the surface area of the box and the volume of the box.

Formula

If the each side of cube is a,

• Its surface area
  `SA = 6a^(2)`

• Its volume
  `V = a^(3)`

`(a-b)^(3)=a^(3)-3a^(2) b+3a^(2) b-b^(3)`

`(a-b)^(2)=a^(2)+b^(2)-2ab`

Now,

Putting
`a =`
`2x-3` we get,

The surface area,
`SA =6(2x-3)^(2)` sq unit

`SA = 6(4x^(2)-12x+9)` sq unit

`SA = 24x^(2) -72x+54` sq unit

And,

The volume,
`V = (2x-3)^(3)` cube unit

`V = 8x^(3)- 36x^(2) +54x-27` cube unit

Hence,

The surface area of the box is
`24x^(2) -72x+54` sq unit and

The volume of the box is
`8x^(3) -36x^(2) +54x-27` cube unit.