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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. - CBSE Class 10 - Mathematics

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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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APPEARS IN

 RD Sharma Solution for 10 Mathematics (2018 to Current)
Chapter 14: Surface Areas and Volumes
Ex. 14.20 | Q: 10 | Page no. 61

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Solution 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. Concept: Surface Areas and Volumes Examples and Solutions.
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