Question

The ratio of radii of a cone and a cylinder having same height is 2 : 3. Then find the
ratio of their volumes.
(A) 4 : 9 (B) 4 : 3 (C) 4 : 27 (D) 27 : 4

Answer 1

${\underline{\boxed{\bf\red{Question}}}}$

The ratio of radii of a cone and a cylinder having same height is 2 : 3. Then find the ratio of their volumes.

(A) 4 : 9

(B) 4 : 3

(C) 4 : 27

(D) 27 : 4

${\underline{\boxed{\bf\red{Answer}}}}$

$\bf\purple{(c) \: { 4:27}}$

$\bf{\underline{\underline\green{Solution}}}$

It is given that, Height of cone and cylinder are same, let be h

Let the radius of cone be 2x

So, radius of cylinder be 3x

Volume of cone : volume of cylinder

$:⟼ \: \bf{ \frac{1}{3}\pi( {2x)}^{2}h :\pi( {3x})^{2}h }$

$:⟼ \: \bf{ \frac{1}{3} \pi4( {x)}^{2} h:\pi9( {x)}^{2} h}$

$:⟼ \: \bf{ \frac{1}{3} \times 4 :9}$

$:⟼ \: \bf{ \frac{4}{3}:9 }$

$:⟼ \: \bf{ 4: 27}$