Question

If the radius of the cone is 6 cm and perpendicular height is 8 cm then find the curved surface area of cone.(take pi=3.14) *​

Answer 1

Given : Radius and Perpendicular height of cone is 6 cm and 8 cm respectively.

To find : Curved surface area (CSA) of cone.

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We require radius and Slant height of cone in the formula of CSA. So, Let's find out the Slant height of cone —

▪︎Formula to find Slant height (l) of cone is given by -

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$\star\:{\underline{\boxed{\pmb{\sf{Slant\:height = \sqrt{\bigg(radius \bigg)^2 + \bigg(height \bigg)^2}}}}}}\\\\\\ \bf{\dag}\:{\underline{\frak{By\:putting\:values\:in\:formula\::}}}\\\\\\ \dashrightarrow\sf Slant\:height = \sqrt{(6)^2 + (8)^2}\\\\\\ \dashrightarrow\sf Slant\:height = \sqrt{36 + 64}\\\\\\ \dashrightarrow\sf Slant\:height = \sqrt{100}\\\\\\ \dashrightarrow{\underline{\boxed{\purple{\pmb{\frak{Slant\:height = 10\:cm}}}}}}\:\bigstar$

$\therefore{\underline{\sf{Slant\:height\:(l)\:of\:cone\:is\:{\pmb{10\:cm}}.}}}$

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✇ Now, By using value of radius (r) & Slant height (l) of cone. Let's find CSA of cone —

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$\qquad\quad\star\:{\underline{\boxed{\pmb{\sf{Curved\:Surface\:Area_{\:(cone)} = \pi r l}}}}}\\\\\\ \qquad\quad\dashrightarrow\sf CSA_{\:(cone)} = 3.14 \times 6 \times 10\\\\\\ \qquad\quad\dashrightarrow\sf CSA_{\:(cone)} = \dfrac{314}{10 \cancel{0}} \times 6 \times \cancel{10}\\\\\\ \qquad\quad\dashrightarrow\sf CSA_{\:(cone)} = 31.4 \times 6\\\\\\ \qquad\quad\dashrightarrow{\underline{\boxed{\pink{\pmb{\frak{CSA_{\:(cone)} = 188.4\:cm^2}}}}}}\:\bigstar$

$\therefore{\underline{\sf{Curved\:Surface\:area\:of\:cone\:is\:{\pmb{188.4\:cm^2}}.}}}$

Answer 2

Answer:

Given :-

• The radius of the cone is 6 cm and perpendicular height is 8 cm.
• π = 3.14

To Find :-

• What is the curved surface area of the cone.

Formula Used :-

$\clubsuit$ Slant Height Formula :

$\longmapsto \sf\boxed{\bold{\pink{l =\: \sqrt{h^2 + r^2}}}}$

where,

• l = Slant Height
• h = Height
• r = Radius

$\clubsuit$ Curved Surface Area of Cone Formula :

$\longmapsto \sf\boxed{\bold{\pink{C.S.A\: Of\: Cone =\: {\pi}rl}}}$

where,

• C.S.A = Curved Surface Area
• r = Radius
• l = Slant Height

Solution :-

First, we have to find the slant height of the cone :

Given :

• Radius = 6 cm
• Height = 8 cm

According to the question by using the formula we get,

$\implies \sf l =\: \sqrt{(8)^2 + (6)^2}$

$\implies \sf l =\: \sqrt{8 \times 8 + 6 \times 6}$

$\implies \sf l =\: \sqrt{64 + 36}$

$\implies \sf l =\: \sqrt{100}$

$\implies \sf\bold{\purple{l =\: 10\: cm}}$

Hence, the slant height is 10 cm .

Now, we have to find the curved surface area of the cone :

Given :

• π = 3.14
• Radius (r) = 6 cm
• Slant Height (l) = 10 cm

According to the question by using the formula we get,

$\longrightarrow \sf C.S.A\: Of\: Cone =\: 3.14 \times 6 \times 10$

$\longrightarrow \sf C.S.A\: Of\: Cone =\: \dfrac{314}{100} \times 60$

$\longrightarrow \sf C.S.A\: Of\: Cone =\: \dfrac{1884\cancel{0}}{10\cancel{0}}$

$\longrightarrow \sf C.S.A\: Of\: Cone =\: \dfrac{1884}{10}$

$\longrightarrow \sf\bold{\red{C.S.A\: Of\: Cone =\: 188.4\: cm^2}}$

$\therefore$ The curved surface area or CSA of cone is 188.4 cm².