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?

A.80pix^3+144pix^2+84pix+16pi
B.20pix^2+26pix+8pi
C.80pix^3+144pix^2+84pix-16pi
D.400pix^4+1040pix^3+996ix^3+416pix+64pi

This is Connexus. Please Help me I am no good at Polynomials.

Answer 1

V= π r^2 h

= π(4x+2)^2 (5x-4)
= π(16x^2 + 16x + 4)(5x-4)
= π(80x^3 - 64x^2 + 80x^2 - 64x + 20x - 16)
= π(80x^3 + 16x^2 - 44x - 16)
= 80πx^3 + 16πx^2 - 44πx - 16π

proof:
h ttps://www.wolframalpha.com/input?i=expand+%CF%80%284x%2B2%29%5E2+%285x-4%29

delete the space at the start of the URL,

none of the given answers are correct