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 = (\pi*r^2*h)/(3)`
Where,
r: radius of the circular base.
h: height
Clearing the radio we have

`r = \sqrt{ (3V)/( \pi*h) }`
Substituting values:

`r = \sqrt{ (3(144\pi))/( \pi*12) }`
Rewriting the obtained equation, we have:

`r = \sqrt{ (432)/(12)}`

`r = √(36)`

`r = 6`
Answer:
the radius of the base of the cone is:

`r = 6`