Question

find the csa of cone whose height is 12 cm and base radius is 5 cm
​

Answer 1

Given

• Height of the cone = 12cm
• Radius of base of the cone = 5cm

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To find

• CSA of the cone.

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Solution

• Firstly we have to find the slant height of the cone.

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

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$\tt\longmapsto{l = \sqrt{(5)^2 + (12)^2}}$

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$\tt\longmapsto{l = \sqrt{25 + 144}}$

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$\tt\longmapsto{l = \sqrt{169}}$

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$\tt\longmapsto{l = 13}$

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• As we know

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$\dag{\boxed{\boxed{\bf{CSA_{(Cone)} = \pi rl}}}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {CSA = \dfrac{22}{7} \times 5 \times 13}$

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$\tt:\implies\: \: \: \: \: \: \: \: {CSA = \dfrac{22 \times 65}{7}}$

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$\tt:\implies\: \: \: \: \: \: \: \: {CSA = \dfrac{1430}{7}}$

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$\frak:\implies\: \: \: \: \: \: \: \: {\underline{\boxed{\purple{CSA = 204.28\: cm^2}}}}$

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Hence,

• The curved surface area of the cone is 204.28 cm².

Answer 2

$\begin{gathered}\bf{\underline{\underline{Given :-}}}\\\end{gathered}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Height = 12cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• Base radius = 5cm

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\begin{gathered}\bf{\underline{\underline{To\:find : - }}}\\\end{gathered}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• CSA of cone ?

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large{\boxed{\boxed{\sf{Solution : - }}}}$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• $\tt\red{★CSA \ of \ cone = πrl }$

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

We know that :-

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⟹ l² = h² + r²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⟹ l² = 12² + 5²

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⟹ l² = 144 + 25

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⟹ l² = 169

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

⟹ l = 13cm

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Coming back to the question,

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ⟹ CSA = πrl

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ⟹ = 22 / 7 x 5 x 13

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

• ⟹ = 204.2 cm²

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⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀

$\large{\boxed{\boxed{\sf{★ CSA \ of \ cone = 204.2cm²}}}}$