Question

The radius of a right circular cone is 3 cm and it's height is 4 cm. The total surface area of the cone is​

Answer 1

Given :

• The radius of a right circular cone = 3 cm

• height = 4 cm

To find :

• Total surface area of the cone

Formula used :

$TSA = \pi \: r(l + r)$

$l = \sqrt{ {r}^{2} + {h}^{2} }$

where :

• TSA = Total surface area
• r = radius
• l = slant height
• π = 22/7
• h = height

Solution :

First we will find out slant height of cone.

$\implies l = \sqrt{ {r}^{2} + {h}^{2} }$

Now put :-

• r = 3 cm
• h = 4 cm

$\implies l = \sqrt{ {(3)}^{2} + {(4)}^{2} }$

$\implies l = \sqrt{ 9 + 16 }$

$\implies l = \sqrt{ 25 }$

$\implies l = \sqrt{ 5 \times 5 }$

$\implies l = 5$

Now we will find TSA of cone :-

$\implies \: TSA = \pi \: r(l + r)$

Now put :-

• r = 3 cm
• h = 4 cm
• l = 5 cm
• π = 22/7

$\implies \: TSA = \dfrac{22}{7} \times 3(5 + 3)$

$\implies \: TSA = \dfrac{22}{7} \times 3 \times 8$

$\implies \: TSA = \dfrac{528}{7}$

$\implies \: TSA = 75.42 \: {cm}^{2}$

Answer :

TSA = 75.42 cm²

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LEARN MORE :-

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

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