Question

A woodworker builds a box as a present for her daughter. The box has a length of 2x + 2, a width of 3x, and a

height of 4x-2 Find the surface area and volume of the box in terms of x.
help me please

Answer 1

Explanation:

Length, L = 2x + 2

Width, W = 3x

Height, H = 4x - 2

`Surface\ Area = 2 (LW + WH + HL)\\\\`

`= 2 ( (2x +2)(3x) + (3x)(4x -2) + (4x - 2)(2x + 2))\\\\=2(6x ^2 + 6x + 12x^2 - 6x + 8x^2 + 8x - 4x - 4)\\\\=2(26x^2 +4x -4) \ square \ units`

`Volume = L * W * H`

`= (2x+2)(3x)(4x-2)\\\\=(6x^2 + 6x)(4x-2)\\\\=24x^3 -12x^2 + 24x^2 - 12x\\\\=24x^3 +12x^2 -12x \ cubic \ units`