Question

A cylinder has a radius of 4x + 2 and a height of 5x + 4. Which polynomial in standard form

best describes the total volume of the cylinder? Use the formula V = 3.14r^2h for the volume of a
cylinder

Answer 1

Explanation:

The volume of a cylinder can be thought of as the area of a circle, scaled by the height of the cylinder. The formula for the volume of a cylinder is:

`V=\pi r^2h`

Plug in the radius, and the height:

`V=\pi (4x+2)^2(5x+4)`

Use FOIL to expand the squared binomial:

`V=\pi (16x^2+16x+4)(5x+4)`

Bring out the binomial to the front of the trinomial:

`V=\pi [(5x+4)(16x^2+16x+4)]`

The process to multiply a trinomial by a binomial involves multiplying the trinomial by each term of the binomial:

`V=\pi [(5x+4)(16x^2+16x+4)]=\pi [5x(16x^2+16x+4)+4(16x^2+16x+4)]`

The rest is just distributing and tedious algebra:

`V=\pi [(80x^3+80x^2+20x)+(64x^2+64x+16)]`

Combine like terms and order the terms from highest exponent to lowest exponent. That is the definition of standard form:

`V=\pi [80x^3+144x^2+84x+16]`

`V=4\pi [20x^3+36x^2+21x+4]`

Answer 2

The answer is A!

Explanation:

area of the base = pi*(4x+2)^2 = pi*(16x^2 +16x +4)

volume of cylinder = pi*r^2 *h

V = pi *(16x^2 +16x +4)(5x+4) = pi*(80x^3 +80x^2 +20x +64x^2 +64x +16) =

= pi*(80x^3 +144x^2 +84x +16)