Question

The volume of a cone of height 5 and radius r is V=5/3πr^2. What is the radius of such a cone whose volume is 2π? r= ______

Answer 1

The volume of a cone with height h=5 is given by,

$V=\frac{5}{3}\pi r^2$

The volume of the above type of cone is given to be V=2π.

So, substitute V=2π in above equation and solve for r.

$\begin{gathered} 2\pi=\frac{5}{3}\pi r^2 \\ \frac{2\cdot3}{5}=r^2 \\ \frac{6}{5}=r^2 \\ r=\sqrt[]{\frac{6}{5}} \\ r=1.095 \end{gathered}$

Therefore, the radius of the cone is 1.095.