Mensuration-43

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A conical hole is drilled in a circular cylinder of height 12 cm and base radius 5 cm. The height
and base of the cone is also the same. Find the whole surface and volume of the remaining cylinder.

Solution: Slant height of the cone = √(52 + 122) = 13 cm

Volume of cylinder = Π x 52 x 12 = 300 Π cm3

Volume of the conical hole = 1/3 x Π x 52 x 12 = 100 Π cm3

Therefore, Volume of the remaining solid

= Volume of the cylinder - Volume of the removed conical part

= 300 Π - 100 Π = 200 Π cm3

Curved surface of the cylinder

= 2 x Π r h = 2 x Π x 5 x 12 = 120 Π cm2

Curved surface of the cone = Π r l = Π x 5 x 13 = 65 Π cm2

Base area of the cylinder = Π x 52 = 25 Π cm2

The whole surface area of the remaining solid includes the curved surface of the cylinder and the cone and also the area of the base

Therefore, Whole surface area = 120 Π + 65 Π + 25 Π = 210 Π cm2

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