Question

A cone with height h and radius r has volume V = 1/3πr^2h. If a certain cone with a height of 6 in. and a volume of V = 8πx^2 + 24πx + 18π, what is its radius r in terms of x?

A. R = 3x + 2
B. 4x^2 + 12x +9
C. 2x + 3
D. (2x + 3) (2x -3)

Which one is the answer? A explanation would be nice too! (Many points!)

Answer 1

Answer: C. 2x+3

Explanation:

`\displaystyle\\V=(\pi r^2h)/(3) \\\\V=(\pi r^2(6))/(3)\\\\V=2\pi r^2\\\\\\8\pi x^2+24\pi x+18\pi \\\\V=2\pi (4x^2+12\pi +9)\\\\V=2\pi ((2x)^2+2(2x)(3)+3^2)\\\\V=2\pi (2x+3)^2\\\\THUS,\\`

`2\pi r^2=2\pi (2x+3)^2`

Divide both parts of the equation by 2π:

`r^2=(2x+3)^2`

Extract the square root of both parts of the equation:

`r=2x+3`