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 the cylinder.

Answer 1

Given-Radius of a sphere $\left(r\right)=4cm$

Also , cylinder whose height is two thirds of its diameter has the same volume as the sphere.

$\therefore$ Volume of the sphere

$=\frac{4}{3}\pi r^3=\frac{4}{3}\pi \times 4\times 4\times 4c{m}^3$
$=\frac{256\pi }{3}c{m}^3$
Now volume of cylinder $=\frac{256\pi }{3}c{m}^3$

According to the question

Let height of the cylinder(h) $=\frac{2}{3}\left(2R\right)=\frac{4}{3}R$
$\therefore$ Volume $=\pi R^{2}H$
$=\pi R^2\times \frac{4}{3}R$
$=\frac{4}{3}\pi R^3\therefore \frac{4}{3}\pi R^3=\frac{256\pi }{3}$
$\Rightarrow R^3=\frac{256\pi }{3}\times \frac{3}{4\pi }=64=(4{)}^3$
$\therefore R=4cm$
Hence radius of the cylinder$=4cm$