Question

a cylinder has a radius of 5x+2 and a height of 4x+8. which polynomial in standard form best describes the total volume of the cylinder? use the formula v=pr^2h for the volume of a cylinder.

Answer 1

Well, the volume of cylinder is:

V = π.r^(2).h

As r = 5x + 2

And,

h = 4x + 8

Then,

V = π . (5x + 2)^(2) . (4x + 8)

Ussing the sum of perfect square

(5x +2)^2 = 25x^2 + 20x + 4

Then,

V = π(25x^2 + 20x + 4).(4x + 8)

Making the distributive

V = π( 100x^3+200x^2+80x^2+160x+16x+32)

V = π( 100x^3 +280x^2+176x+32)

V = 2π.( 50x^3 + 140x^2 + 88x+16)

V = 4π.( 25x^3 + 70x^2+44x+8)