Answer:
B
Step-by-step explanation:
We are given a cylinder with a height of (2x + 7) and a radius of (x - 3).
And we want to find the expression for the volume of the cylinder.
Recall that the volume of a cylinder is given by:
[tex]\displaystyle V = \pi r^2 h[/tex]
Where r is the radius and h is the height.
Substitute:
[tex]\displaystyle V = \pi(x-3)^2(2x+7)[/tex]
Expand. We can use the perfect square trinomial pattern:
[tex]\displaystyle V = \pi \left[\underbrace{(x^2-6x+9)}_{(a-b)^2=a^2-2ab+b^2}(2x+7)\right][/tex]
Distribute:
[tex]V=\pi \left[ 2x(x^2-6x+9)+7(x^2-6x+9)\right][/tex]
Distribute:
[tex]V = \pi \left[(2x^3-12x^2+18x)+(7x^2-42x+63)\right][/tex]
Rewrite:
[tex]V = \pi\left[(2x^3)+(-12x^2+7x^2)+(18x-42x)+(63)\right][/tex]
Combine like terms:
[tex]V = \pi (2x^3-5x^2-24x+63)[/tex]
Distribute:
[tex]V = 2\pi x^3-5\pi x^2 -24\pi x+63\pi[/tex]
Hence, our answer is B.
