Question

Challenge: find the radius of the base of a cone with volume equal to 144π in3 and height equal to 12 in.

Answer 1

By definition, the volume of a cone is given by:
 $V = \frac{\pi*r^2*h}{3}$
 Where,
 r: radius of the circular base.
 h: height
 Clearing the radio we have
 $r = \sqrt{ \frac{3V}{ \pi*h} }$
 Substituting values:
 $r = \sqrt{ \frac{3(144\pi)}{ \pi*12} }$
 Rewriting the obtained equation, we have:
 $r = \sqrt{ \frac{432}{12}}$
 $r = \sqrt{36}$
 $r = 6$
 Answer:
 the radius of the base of the cone is:
 $r = 6$