Question

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

Answer 1

Step-by-step explanation:

★Given -

• A cylinder and cone have bases of equal radii and are of equal heights.

★To prove -

• Show that their volumes are in the ratio of 3:1.

★Solution -

$\rm{Volume \: of \: cylinder = πr²h}$

$\rm{Volume \: of \: cone = \dfrac{1}{3} πr²h}$

$\rm{ \normalsize{Now, ratio} = \: \large \frac{Volume \: of \: cylinder}{Volume \: of \: cone} }$

$\longmapsto \rm{ \dfrac{ \cancel{\pi {r}^{2} h}}{ \dfrac{1}{3} \: \cancel{\pi {r}^{2} h} }}$

$\longmapsto \rm{ \dfrac{1}{ \dfrac{1}{3} } }$

$\longmapsto \rm{ \dfrac{3}{1} }$

$\rm{ \orange{Therefore, the \: ratio \: is \: 3:1 , \: hence \: proved }}$