Question

The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is 5 cm, then height of the cone is
(a)10 cm
(b)15 cm
(c)18 cm
(d)24 cm

Answer 1

$\mathfrak\pink{Question}$

The material of a cone is converted into the shape of a cylinder of equal radius. If height of the cylinder is 5 cm, then height of the cone is

(a)10 cm

(b)15 cm

(c)18 cm

(d)24 cm

$\mathfrak\orange{Answer}$

$\bold{Height \:of\: the\: cylinder=5\:cm}$

$\bold{Volume \: of \: cylinder}=\bold{2 \pi \: r {}^{2}h }=$

$\bold{Volume \: of \: cone}= \bold{ \frac{1}{3}\pi \: r {}^{2} h }$

Now,

$\mathfrak\orange{To,\:find\:the\: height\:of\:the\:cone}$

$h = \bold{ \frac{1}{3}\pi \times r {}^{2} \times h }=\bold{ \pi \: r {}^{2} \times 5}$

$→h = 15 \: cm$

Therefore,

$\mathfrak\purple{Option\:A\:is \:the\:answer}$

Answer 2

Answer :- Option (B) 15 cm

Explanation :-

Given :-

The height of cone = ?

The height of cylinder is 5 cm.

The radius of cone = Radius of cylinder

Volume of cone :-

$\bold{\frac{1}{3} \pi \:r^{2} h_{1} }$

Volume of cylinder :-

$\bold{\pi \: {r}^{2} h_{2} }$

Since the volume are equal,

$\bold{\frac{1}{3} \pi \:r^{2} h_{1} = \pi \: {r}^{2} h_{2} }$

$\bold{\frac{1}{3} \pi \:r^{2} h_{1} = \pi \: {r}^{2} 5 }$

$\bold{\frac{ h_{1} }{3} = h_{2} }$

$\bold{ \frac{ h_{1} }{3} = 5}$

$\bold{h_{1} = 5 \times 3}$

$\bold{ h_{1} = 15 \: cm}$

Therefore, the height of the cone is 15 cm respectively.