A cone with height h and radius r has volume V = 13πr^2h. If the cone has a height of 6 in. and volume V = 8πx^2 + 24πx + 18π, what is its radius r in terms of x?

Question

r=3x+2 or

r=4x^2+12x+9 or

r=2x+3 or

r=(2x+3)(2x-3)

Answer 1

V= (1/3)pi(r)^2h = (1/3)pi(r^2)6 = 2pi(r)^2 = 8pix^2 +24pix + 18pi

divide 2pi to get

r^2 = 4x^2 + 12x + 9

r = the square root of (4x^2 + 12x +9) = sqr(2x+3)^2

r = 2x+3