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:-

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

To Find:-

• Curved surface area of Cone.

Formula Used:-

• ${\boxed{\bf{CSA\:of\:Cone=\pi rl}}}$

• ${\boxed{\bf{l=\sqrt{r^2+h^2}}}}$

Here,

• r = Radius

• l = Slant Height

• h = Perpendicular Height

Solution:-

Firstly,

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

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

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

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

$\bf :\implies\:l=10\:cm$

Now,

$\bf :\implies\:CSA\:of\: Cone=\pi rl$

$\sf :\implies\:CSA\:of\: Cone=3.14\times6\times10$

$\bf :\implies\:CSA\:of\: Cone=188.4\:cm^2$

Hence, The Curved Surface Area of the Cone is 18.4cm².

━━━━━━━━━━━━━━━━━━━━━━━━━

Answer 2

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 :-

♣ Slant Height Formula :

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

where,

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

♣ Curved Surface Area of Cone

Formula :

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

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,

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

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

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

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

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

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,

$\begin{gathered}\longrightarrow \sf C.S.A\: Of\: Cone =\: 3.14 \times 6 \times 10\\\end{gathered}$

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

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

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

∴ The curved surface area or CSA of cone is 188.4 cm².