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

Answer:

1960 (3 s.f)

Step-by-step explanation:

the formula of curved surface area for cone is pi×height×length

1. to find length:

length^2 = 10^2 × 24^2 (pythagoras theorem)

length^2 = 676

length = 26

2. to find C.S.A.

pi×24×26 = 1960.353816

= 1960 (3 s.f.)

Answer 2

Given:

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

Need to find:

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

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

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Therefore,

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

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

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

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

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where,

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

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Therefore,

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

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

⠀⠀⠀⠀━━━━━━━━━━━━━━━━━━━━━⠀⠀⠀⠀⠀

$\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\blue{\bigstar\: Formulae\:related\:to\:cone :}}}}}\mid}$⠀

• $\sf Area\:of\:base = \bf{\pi r^2}$

• $\sf Curved\:surface\:area\:of\:cone = \bf{\pi rl}$

• $\sf Total\:surface\:area\:of\:cone = Area\:of\:base + CSA = \pi r^2 + \pi rl = \bf{\pi r(r + l)}$

• $\sf Volume\:of\:cone = \bf{\dfrac{1}{3} \pi r^2 h}$