Question

if the slant height of the cone is 21 cm and diameter of its base is 24cm the total service area of cone is​

Answer 1

Answer:

490.285714

Step-by-step explanation:

given

slant height of cone=21cm

diameter of it's base =24cm

radius =diameter/2

=24/2=12

total surface area of cone is π r(r+l)

22/7(12)(12+1)

490.285714

Answer 2

$\setlength{\unitlength}{1.8mm}\begin{picture}(5,5)\thicklines\put(0,0){\qbezier(1,0)(12,3)(24,0)\qbezier(1,0)(-2,-1)(1,-2)\qbezier(24,0)(27,-1)(24,-2)\qbezier(1,-2)(12,-5)(24,-2)}\put(-0.5,-1){\line(1,2){13}}\put(25.5,-1){\line(-1,2){13}}\multiput(12.5,-1)(2,0){7}{\line(1,0){1}}\multiput(12.5,-1)(0,4){7}{\line(0,1){2}}\put(15,0){\sf{12 cm}}\put(22,10){\sf{21 cm}}\end{picture}$

⠀

$\sf Given \begin{cases} & \sf{Slant\; Height,\;l = 21\;cm} \\ & \sf{Diameter,\;d = 24\;cm} \\ & \sf{Radius,\;r = 24/2 = 12\;cm} \end{cases}$

Need to find: Total surface area of cone.

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We know that,

⠀

$\star\;{\boxed{\sf{\purple{Total\:surface\;area_{\;(cone)} = \pi r(r + l)}}}}$

Putting values,

⠀

$:\implies\sf \dfrac{22}{7} \times 12 \bigg(12 + 21\bigg)$

$:\implies\sf \dfrac{22}{7} \times 12 \times 33$

$:\implies{\boxed{\sf{\pink{1244.57\;cm^2}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Hence,\;Total\: surface\;area\;of\;cone\;is\; \bf{1244.57\;cm^2}.}}}$

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$\boxed{\underline{\underline{\bigstar \: \bf\:Formula\:Related\:to\:Cone\:\bigstar}}}$

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$\sf (i)\;Curved\;Surface\;Area\;of\;cone\; = \; \red{\pi rl}$

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$\sf (ii)\;Total\; surface\;area\;of\;cone\; = \; \purple{\pi r(r + l)}$

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$\sf (iii)\;Area\;of\;base\;of\;cone\; = \; \green{\pi r^2}$

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$\sf (iv)\;Volume\;of\;cone\; = \; \pink{ \dfrac{1}{3} \pi r^2h}$