Question

The volume of the cone is 243π ft3 what is the radius of the cone

Answer 1

The volume of a cone is given by

`V=(1)/(3)\pi r^2h`

where r is the radius and h is the height of our cone. Since we want the radius, we need to isolate r in this formula. Then, by moving 3 to the left hand side, we have

`3\cdot V=\pi r^2h`

now, by movinf Pi and h to the left hand side, we have

`(3V)/(\pi h)=r^2`

and finally, r is given by

`r\questeq\sqrt[]{(3V)/(\pi h)}`

Now, we can substitute the given values, V=243Pie, h= 9 and get

`r=\sqrt[]{(3(243\pi))/(\pi(9))}`

We can note that we can cancel out Pie because this number is on the numerator and denominator, then we have

`r=\sqrt[]{(3(243))/(9)}`

which gives

`\begin{gathered} r=\sqrt[]{81} \\ r=9 \end{gathered}`

therefore, the radius measure 9 feet.