Question

The washer base has an area of 6x2 -2 -28 with aheight of 2x + 4. Find the volume of the washer.

Answer 1

We have to calculate the volume V of the washer.

This can be calculated as the product of the base B and the height H, and B and H are defined in function of x, so we will have a volume V that will be a function of x too.

We can calculate this as:

$\begin{gathered} V=B\cdot H \\ V=(6x^2-2x-28)(2x+4) \\ V=6x^2\cdot2x+6x^2\cdot4+(-2x)(2x)+(-2x)\cdot4+(-28)\cdot2x+(-28)\cdot4 \\ V=12x^3+24x^2-4x^2-8x-56x-112 \\ V=12x^3+20x^2-64x-112 \end{gathered}$

We have applied the distributive property and group the similar terms together.

The volume is 12x^3+20x^64x-112.