Question

From a solid cylinder of height and radius 8 and 6 cm, a conical cavity of same height and radius is hollowed out. Find the Total surface area of the remaining solid l. (Take π=3.14)

Answer 1

Answer:

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Answer 2

$\huge\underline\mathrm{Answer-}$

$\large{\boxed{\red{\rm{TSA\:of\:remaining\:solid\:=\:602.88\:cm^2}}}}$

$\huge\underline\mathrm{Explanation-}$

Given :

• height of cylinder = 8 cm
• radius of cylinder = 6 cm
• height of cone = 8 cm
• radius of cone = 6 cm

To find :

• Total surface area ( TSA ) of remaining solid.

Solution :

$\boxed{\sf{TSA\:of\:remaining\:solid\:=\:CSA\:of\:cylinder\:+\:CSA\:of\:cone\:+\:Area\:of\:circlular\:opening}}$

$\implies$ TSA of remaining solid = 2πrh + πrl + πr²

$\implies$ TSA of remaining solid = πr ( 2h + l + r )

$\rule{200}2$

We have to calculate slant height ( l )

L² = h² + r²

$\implies$ L² = 8² + 6²

$\implies$ L² = 64 + 36

$\implies$ L² = 100

$\implies$ L = √100

$\implies$ L = 10 cm

$\rule{200}2$

Now putting the values,

$\implies$ TSA of remaining solid = (3.14)(6)[(2×8) + 10 + 6 ]

$\implies$ TSA of remaining solid = 18.84 ( 16 + 16 )

$\implies$ TSA of remaining solid = 18.84 ( 32 )

$\large{\boxed{\red{\rm{\therefore\:TSA\:of\:remaining\:solid\:=\:602.88\:cm^2}}}}$