Question

find the total surface area of a cone if it's slant height is 23m and diameter of its base is 24m​

Answer 1

Given that,

• Slant Height of the cone is 23 m.
• Diameter of its Base is 24 m.

Need to find:

• The TSA(total surface area) of cone.

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$\setlength{\unitlength}{1.6mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(16,1.6){\sf{12 m}}\put(22,10){\sf{23 m}}\end{picture}$

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Solution: Finding Radius (r) = 24/2 = 12 m.

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

$\star\;\boxed{\sf{\pink{TSA_{\:(cone)} = \pi r(r + l)}}}$

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where,

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

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Therefore,

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$:\implies\sf TSA_{\;(cone)} = \bigg(\dfrac{22}{7} \times 12(12 + 23)\bigg) \\\\\\:\implies\sf TSA_{\;(cone)} = \bigg(\dfrac{22}{7} \times 12 \times 35\bigg) \\\\\\:\implies{\underline{\boxed{\frak{\pink{ TSA_{\;(cone)} = 1320\;m^2}}}}}\;\bigstar$

$\therefore{\underline{\sf{Hence, \;TSA\; of \; cone \; is \; \bf{1320\;m^2 }.}}}$

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

• $\sf Area\:of\:base = \bf{\pi r^2}$

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

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

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

Answer 2

Total surface area of a cone

= 7Tr(r+1)

= (12)(12+21)

= 121(33) =

= 3961

= 396(3.14)

= 1243.44

Hence, the answer is 1243.44m2