from a solid cylinder whose height is 16 cm and radius is 12 cm a conical cavity of height 8cm and base radius 6cm is dug out find the total surface area of remaining solid
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Answer:
TSA of remaining solid = 2187.43 cm²
Step-by-step explanation:
TSA of Cylinder
= 2πr (h+r)
= 2 × 22/7 × 12 (16+12)
= 2112 cm²
Since circular base of the cone is common among the two shapes, it needs to be subtracted.
TSA of Cylinder - Area of circular base of Cone
= 2112 - πr²
= 2112 - (22/7 × 6 × 6)
= 2112 - 113.14
= 1998.86 cm²
Since circular base has been subtracted, we only need to find CSA of the Cone.
CSA of Cone = πrl
l = √h²+r²
= √64+36
= √100
= 10 cm
CSA of the Cone
= πrl
= 22/7 × 6 × 10
= 188.57 cm²
Hence, TSA of the remaining solid
= 1998.86 + 188.57
= 2187.43 cm²
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