Question

An empty box is in the shape of the cylinder surmounted by a conical top. If radion of box is 12 cm, slant height of the conical part is 13 cm and height of the cylinder is 11 e then find the total surface area of this empty box. (A cover is not fitted.)




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Answer 1

FINAL ANSWER:-

$773.14cm^{2}$

GIVEN:-

• An empty box is in the shape of the cylinder surmounted by a conical top

• radius of box as well as cone(r) = $6cm$

• height of cylinder(h) =  $11cm$

• slant height of cone(l) = $13cm$

TO FIND:-

the total surface area of this empty box

THINGS TO KNOW:-

empty box consist of a outer cone (CSA) + base of box of cylindrical shape  (CSA) + πr²

SOLUTION:-

here dimensions are-

$\pi = \frac{22}{7}\\r= 6cm\\h= 11cm\\l= 13cm$

the total surface area of this empty box = CSA of cone + CSA of cylinder + πr²

$=\pi rl+2\pi rh+ \pi r^{2} \\=13*6 *\pi + 2*\pi *6*11 + \pi *6*6\\=78\pi + 132\pi + 36\pi \\=(246) \pi \\=246* \frac{22}{7} \\=773.14\:cm^{2}$

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some important formulas are :-

$TSA\:of\:cylinder=2\pi rh +2\pi r^{2}\\TSA\:of\:hemisphere=3\pi r^{2}\\TSA\:of\:sphere=4\pi r^{2}\\TSA\:of\:cone=\pi r(r+l)\:\:or \:\:\pi rl + \pi r^{2}\\TSA\:of\:cube=6s^{2}\\TSA\:of\:cuboid=2(lb+lh+bh)$

$CSA\:of\:cylinder=2\pi rh\\CSA\:of\:hemisphere=2\pi r^{2}\\CSA\:of\:sphere=4\pi r^{2} (same\:as\:TSA\:of\:sphere)\\CSA\:of\:cone=\pi rl\\CSA\:of\:cube=4s^{2}\\CSA\:of\:cuboid=2(lb+bh)$