[tex]r(v) = \sqrt{\frac{3v}{20 \pi }}\ inches[/tex]
Solution:
The volume of cone is given as:
[tex]v = \frac{1}{3}\pi r^{2} h[/tex]
Where,
r is the radius
h is the height
From given,
height = 20 inches
From formula,
[tex]v = \frac{1}{3}\pi r^{2} h[/tex]
Rearrange , so that r is alone in left side of equation
[tex]3v = \pi r^2 h\\\\\pi r^2 h = 3v\\\\r^2 = \frac{3v}{\pi h}\\\\Take\ square\ root\ on\ both\ sides\\\\r = \sqrt{\frac{3v}{\pi h}}[/tex]
Substitute h = 20
[tex]r = \sqrt{\frac{3v}{20 \pi }}[/tex]
Thus, radius as function of volume is:
[tex]r(v) = \sqrt{\frac{3v}{20 \pi }}\ inches[/tex]
