Question

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

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.