Question

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.

Answer 1

surface area = 210 π cm²

Radius of cylinder(r) = 5 cm 

Height of cylinder, (h) = 12 cm

 Let, l be slant height of cone 

l = \(\sqrt{r^2 + h^2}\)

Slant height of the cone = \(\sqrt{5^2 + 12^2}\) =13 cm 

Volume of cylinder = π × 5²× 12 = 300 cm³ 

Volume of the conical hole = \(\frac{1}3\) × 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 = 25 cm² 

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