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

$V=\frac{1}{3}\pi r^2h$

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

$\frac{3V}{\pi h}=r^2$

and finally, r is given by

$r\questeq\sqrt[]{\frac{3V}{\pi h}}$

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

$r=\sqrt[]{\frac{3(243\pi)}{\pi(9)}}$

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

$r=\sqrt[]{\frac{3(243)}{9}}$

which gives

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

therefore, the radius measure 9 feet.