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

Height of cylinder, (h) = 12 cm

Let, l be slant height of cone Slant height of the cone = =13 cm

Volume of cylinder = π × × 12 = 300 cm3

Volume of the conical hole = × π × 5 × 12 = 100 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 × π r h = 2 × π × 5 × 12 = 120π cm

Curved surface of cone = π r l = π × 5 × 13 = 65π cm

Base area of cylinder = π × 52 = 25cm2

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

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

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