Question

A cylinder whose height is two thirds of its diameter, has the same volume as a sphere of radius 4 cm. Calculate the radius of the base of cylinder.

Answer 1

Let r be the radius and h be the height of the cylinder . Then,

$h=\frac{2}{3}\left(Diameter\right)=\frac{2}{3}\times 2r=\frac{4r}{3}$

Now,

Volume of the cylinder = Volume of the sphere of radius 4 cm

$\pi r^{2}h=\frac{4}{3}\pi \times (4{)}^3$

$\pi r^2\times \frac{4r}{3}=\frac{4\pi }{3}\times 4^3$

$r^3=4^3$

$r=4$ $cm$