Question

The height and the slant height of a cone are 21cm and 28 cm respectively. Find the volume of the cone.​

Answer 1

Given :

• Height and Slant Height of a Cone are 21 cm and 28 cm respectively .

To Find :

• Volume of Cone

Solution :

$\longmapsto\tt{Height(h)=21\:cm}$

$\longmapsto\tt{Slant\:Height(l)=28\:cm}$

Firstly we will find Radius of Cone :

$\longmapsto\tt{{(l)}^{2}={(r)}^{2}+{(h)}^{2}}$

$\longmapsto\tt{{(28)}^{2}={(r)}^{2}+{(21)}^{2}}$

$\longmapsto\tt{784={(r)}^{2}+441}$

$\longmapsto\tt{784-441={(r)}^{2}}$

$\longmapsto\tt{\sqrt{373}=r}$

$\longmapsto\tt\bf{7\sqrt{7}=r}$

So , The Radius of Cone is 7√7 cm ....

Now ,

$\longmapsto\tt{Height(h)=21\:cm}$

$\longmapsto\tt{Radius(r)=7\sqrt{7}\:cm}$

Using Formula :

$\longmapsto\tt\boxed{Volume\:of\:Cone=\dfrac{1}{3}\pi{{r}^{2}h}}$

Putting Values :

$\longmapsto\tt{\dfrac{1}{3} \times\dfrac{22}{7} \times{7\sqrt{7}}\times{7\sqrt{7}}\times{21}}$

$\longmapsto\tt{\dfrac{22\times{343}\times{{\cancel{3}}}}{{\cancel{3}}}}$

$\longmapsto\tt\bf{7546\:{cm}^{3}}$

So , The Volume of Cone is 7546 cm³ ....

Answer 2

$\LARGE\underline{\underline{\pink{\sf Given:}}}$

⚝ Slant Height, l = 28cm

⚝ Height of Cone, h = 21cm

$\LARGE\underline{\underline{\pink{\sf Find:}}}$

⛥ What is the volume of Cone

$\LARGE\underline{\underline{\pink{\sf Solution:}}}$

Let, the radius of Cone be r cm

we, know that

$\boxed{ \sf {l}^{2} = {r}^{2} + {h}^{2} }$

where,

• l = 28cm
• h = 21cm

So,

$\to\sf {l}^{2} = {r}^{2} + {h}^{2}$

$\to\sf {(28)}^{2} = {r}^{2} + {(21)}^{2}$

$\to\sf 784= {r}^{2} + 441$

$\to\sf 784 - 441 = {r}^{2}$

$\to\sf 343 = {r}^{2}$

$\to\sf r = \sqrt{343}$

$\to\sf r = \sqrt{49 \times 7}$

$\to\sf r = 7\sqrt{7}cm$

So, radius = 7√7 cm

__________________

we, know that

$\boxed{ \sf Volume \: of \: Cone = \dfrac{1}{3} \pi {r}^{2}h}$

where,

• π = 22/7
• r = 7√7 cm
• h = 21cm

So,

$\to\sf Volume \: of \: Cone = \dfrac{1}{3} \pi {r}^{2}h$

$\to\sf Volume \: of \: Cone = \dfrac{1}{3} \times \dfrac{22}{7} {(7 \sqrt{7})}^{2} \times 21$

$\to\sf Volume \: of \: Cone = \dfrac{22}{21} (49 \times 7)\times 21$

$\to\sf Volume \: of \: Cone = \dfrac{22}{21} (343\times 21)$

$\to\sf Volume \: of \: Cone = \dfrac{22}{21} (7203)$

$\to\sf Volume \: of \: Cone = \cancel{\dfrac{158466}{21}} = 7546cm$

$\to\sf Volume \: of \: Cone = 7546 {cm}^{3}$

$\small{ \sf\therefore volume \: of \: cone \: 7546 {cm}^{3} }$