# Mensuration-43

### From Homeworkwiki

**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 = √(5^{2} + 12^{2}) = 13 cm

Volume of cylinder = Π x 5^{2} x 12 = 300 Π cm^{3}

Volume of the conical hole = 1/3 x Π x 5^{2} x 12 = 100 Π cm^{3}

Therefore, Volume of the remaining solid

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

= 300 Π - 100 Π = 200 Π cm^{3}

Curved surface of the cylinder

= 2 x Π r h = 2 x Π x 5 x 12 = 120 Π cm^{2}

Curved surface of the cone = Π r l = Π x 5 x 13 = 65 Π cm^{2}

Base area of the cylinder = Π x 5^{2} = 25 Π cm^{2}

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 cm^{2}