Question

a conical tent is 10m high and the radius of its base is 24m find the cuved surface area of the tent ​

Answer 1

$\large\underline\bold\red{Given:-}$

A conical tent is 10 m high, Height (h) = 10m. And, the radius of its base is 24 m, radius (r) = 24m.

$\large\underline\bold\red{To\:Find:-}$

• The CSA(Curved surface area) of the conical tent.

$\large\underline\bold\red{Solution:-}$

Finding slant Height of the conical tent, let slant height be l .

Therefore,

$:\implies\sf (l)^2 = (h)^2 + (r)^2 \\\\\\:\implies\sf l^2 = 10^2 + 24^2 \\\\\\:\implies\sf l^2 = 100 + 576\\\\\\:\implies\sf l^2 = 676\\\\\\:\implies\sf l = \sqrt{676}\\\\\\:\implies{\underline{\boxed{\frak{\pink{l = 26\;m}}}}}\;\bigstar$

⠀

$\therefore{\underline{\sf{Hence, \; slant\; height\; of \; conical\; tent \; is \; \bf{26\;m }.}}}$⠀⠀

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⠀

$\large{\underline\bold\red{\tt{As\;we\;know\;that,}}}$

⠀

$\star\;\boxed{\sf{\purple{CSA_{\:(cone)} = \pi rl}}}$

⠀

where,

r is the radius of the cone and l is the slant Height of the cone.

Therefore,

$:\implies\sf CSA_{\:(tent)} = \bigg(\dfrac{22}{7} \times 24 \times 26\bigg)\\\\\\:\implies\sf CSA_{\:(tent)} = \bigg(\dfrac{22}{7} \times 624 \bigg)\\\\\\:\implies{\underline{\boxed{\tt{\red{ CSA_{\:(tent)} = 1961\;m^2}}}}}\;\bigstar$

⠀

$\therefore{\underline\red{\sf{Hence, \;CSA\; of \; conical\; tent \; is \; \bf{1961\;m^2 }.}}}$⠀⠀

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Answer 2

$\large\underline{\tt\red{Given:- }}$

A conical tent is 10 m high, Height (h) = 10m. And, the radius of its base is 24 m, radius (r) = 24m.

$\tt\large\underline{\red{To\:find:- }}$

• The CSA(Curved surface area) of the conical tent.

$\large\underline\bold\red{Solution:-}$

Finding slant Height of the conical tent, let slant height be l .

Therefore,

$:\implies\sf (l)^2 = (h)^2 + (r)^2 \\\\\\:\implies\sf l^2 = 10^2 + 24^2 \\\\\\:\implies\sf l^2 = 100 + 576\\\\\\:\implies\sf l^2 = 676\\\\\\:\implies\sf l = \sqrt{676}\\\\\\:\implies{\underline{\boxed{\frak{\green{l = 26\;m}}}}}\;\bigstar$

⠀

$\therefore{\underline{\sf{Hence, \; slant\; height\; of \; conical\; tent \; is \; \bf{26\;m }.}}}$⠀⠀

$\rule{250px}{.3ex}$⠀⠀⠀

⠀

$\tt{\large{\pink{We\:know\:that}} }$

⠀

$\star\;\boxed{\sf{\orange{CSA_{\:(cone)} = \pi rl}}}$

⠀

where,

r is the radius of the cone and l is the slant Height of the cone.

Therefore,

$:\implies\sf CSA_{\:(tent)} = \bigg(\dfrac{22}{7} \times 24 \times 26\bigg)\\\\\\:\implies\sf CSA_{\:(tent)} = \bigg(\dfrac{22}{7} \times 624 \bigg)\\\\\\:\implies{\underline{\boxed{\tt{\red{ CSA_{\:(tent)} = 1961\;m^2}}}}}\;\bigstar$

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