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.]
Volume of the remaining solid = Volume of cylinder - volume of the cone
Volume of the remaining solid =πr2h−13πr2h=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