In the given figure from the top of a solid cone of hieght 12 cm and base radius 6 cm ,a cone of height 4 cm is removal by a plane parallel to the base. find the T.S.A of the remaining solid (useπ=3.14)
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Answer:
The TSA of the remaining solid is 344 cm²
Step-by-step explanation:
slant height l of full cone ,
l = √(h²+r²) = √(12²+6²) = √180 = 13.41
hence surface area of curved surface of larger cone = πrl
= 3.14 x 6 x 13.41
= 252.76 cm²
radius of the smaller cone
r₁ = r(h₁/h) = 6(4/12) = 2 cm
slant height of smaller cone = l₁ = √(h₁² + r₁²) = √(16 + 4) = √20 = 4.47
Hence curved surface area of smaller cone = πr₁l₁
= 3.14 x 2 x 4.47
= 28.08 cm²
Hence curved surface area of the remaining portion = 252.76 - 28.08
= 224.68
Hence the total surface area of the remaining solid
= curved surface area + πr² + πr₁²
= 224.68 + 3.14 x 36 + 3.14x2
= 224.68 + 113.04 + 6.28
= 344 cm²
Hence the TSA of the remaining solid is 344 cm²
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