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

Given that:

r = 5 cm

h = 12 cm

We have the following diagram

Slant height of cone is given by

`l=sqrt(r^2+h^2)`

`=sqrt(5^2+12^2`

= 13 cm

The total surface area of the remaining part is given by

`S=2pirh+pir^2+pirl`

`2xxpixx5xx12+pixx5^2+pixx5xx13`

= 120π+25π+65π

=210π cm²

The volume of the remaining part is given by

`V=pir^2h-1/3pir^2h`

`=2/3pir^2h`

`=2/3xxpixx5^2xx12`

= 200π cm³

Hence, S =210π cm². V = 200π cm³