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Question

From a solid cylinder whose height is 8 cm and radius 6 cm, a conical cavity of height 8 cm and of base radius 6 cm is hollowed out. Find the volume of the remaining solid. Also, find the total surface area of the remaining solid. [Take π=3.14.]


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Solution

Volume of the remaining solid = Volume of cylinder - volume of the cone

Volume of the remaining solid =πr2h13πr2h=23πr2h=23×3.14×(6)2×8=603.19 cm3

Slant height of cone, AB=BC2+AC2=82+62=64+36=10 cm

Total surface area of the remaining solid = curved surface area of cylinder + area of base of cylinder + curved surface area of cone
=2πrh+πr2+πrl=2π×6×8+π×62+π×6×10=96π+36π+60π=192π=192×3.14=603.19 cm2


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