Question

A cylinder and cone have base of equal radii and are of equal heights. Show that their volumes are in the ratio of 3 : 1.

Answer 1

Given,
Radius of Cylinder = Radius of Cone
Also, Height of Cylinder = Height of Cylinder

Formulae used :

$\boxed{\mathbf{Volume \: of \: Cylinder = π {r}^{2}h}}$

$\boxed{\mathbf{Volume \: of \: Cone = \frac{1}{3}π{r}^{2}h}}$

$\underline{\underline{\huge\mathfrak{Solution}}}$

$\bf \frac{Volume \: of \: Cylinder}{Volume \: of \: Cone} \\ \\ = \frac{\pi {r}^{2} h}{ \frac{1}{3}\pi {r}^{2} h } \\ \\ = \frac{ {r}^{2} h}{ \frac{1}{3} {r}^{2} h } \\ \\ \bf Since \: the \: radius \: and \: height \: of \: \\ \bf both \: is \: equal \\ \\ \frac{1}{ \frac{1}{3} } \: i.e. \: 1 : \frac{1}{3} \\ \\ \bf Multiplying \: 3 \\ \\ = 3(1 : \frac{1}{3} )$


$\boxed{\mathbf{3 : 1}}$

Hence Proved!