Question

The area if the base of a right circular cone is 81cm2 and it's height is 12cm. what is the curved surface area in cm2 of the cone?
$\pi$
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Answer 1

Given :-

• Area of base of cone = 81 sq. cm

• Height of cone = 12 cm

To Find :-

• Curved Surface Area of cone

Formula Used :-

$\boxed{ \sf{ \: Area_{(base)} \: = \: \pi \: {r}^{2}}}$

$\boxed{ \sf{ \: CSA_{(cone)} \: = \: \pi \: r \: l}}$

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

where

• r is radius of cone

• l is slant height of cone

• h is height of cone.

Solution :-

Given that

Base area of cone = 81

$\rm :\longmapsto\:\pi {r}^{2} = 81$

$\rm :\longmapsto\: {r}^{2} = \dfrac{81}{\pi}$

$\rm :\longmapsto\:r = \dfrac{9}{ \sqrt{\pi} } \: cm$

Now,

Slant height of cone is

$\rm :\longmapsto\: {l}^{2} = {r}^{2} + {h}^{2}$

$\rm :\longmapsto\: {l}^{2} = \dfrac{81}{\pi} + {12}^{2}$

$\rm :\longmapsto\: {l}^{2} = \dfrac{81}{\pi} + 144$

$\rm :\longmapsto\: {l}^{2} = \dfrac{81 + 144\pi}{\pi}$

$\bf\implies \:l = \sqrt{\dfrac{81 + 144\pi}{\pi} }$

Now,

Curved Surface Area of Cone is

$\rm :\longmapsto\:CSA_{(cone)} = \pi \: r \: l$

$\rm :\longmapsto\:CSA_{(cone)} = \pi \: \times \dfrac{9}{ \sqrt{\pi} } \times \sqrt{\dfrac{81 + 144\pi}{\pi} }$

$\rm :\longmapsto\:CSA_{(cone)} = 9 \times \sqrt{81 + 144\pi}$

$\rm :\longmapsto\:CSA_{(cone)} = 9 \times \sqrt{81 + 144 \times 3.14}$

$\rm :\longmapsto\:CSA_{(cone)} = 9 \times \sqrt{81 + 452.16}$

$\rm :\longmapsto\:CSA_{(cone)} = 9 \times \sqrt{533.16}$

$\rm :\longmapsto\:CSA_{(cone)} = 9 \times 23.09$

$\bf :\longmapsto\:CSA_{(cone)} = 207.81 \: {cm}^{2}$

Additional Information :-

Volume of cylinder = πr²h

T.S.A of cylinder = 2πrh + 2πr²

Volume of cone = ⅓ πr²h

C.S.A of cone = πrl

T.S.A of cone = πrl + πr²

Volume of cuboid = l × b × h

C.S.A of cuboid = 2(l + b)h

T.S.A of cuboid = 2(lb + bh + lh)

C.S.A of cube = 4a²

T.S.A of cube = 6a²

Volume of cube = a³

Volume of sphere = 4/3πr³

Surface area of sphere = 4πr²

Volume of hemisphere = ⅔ πr³

C.S.A of hemisphere = 2πr²

T.S.A of hemisphere = 3πr²

Answer 2

Answer:

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