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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.
Solution
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
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