Question

A cone with height h and radius r has volume V = 13πr2h. If a certain cone with a height of 9 inches has volume V = 3πx2 + 42πx + 147π, what is the cone’s radius r in terms of x?

Answer 1

$\fontsize{18}{10}{\textup}{\textbf{The value of r is (x+7)/sqrt(39)}}}$

Step-by-step explanation:

Given V=13*pi*r^2*h

When h=9

then V=3pi*x^2+42pi*x+147pi=13*pi*r^2*9

=>3x^2+42x+147=117r^2

=>x^2+14x+49=39r^2

=>(x+7)^2=39r^2

=>r=(x+7)/sqrt(39)