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Question
The height of a solid cylinder is 15 cm and the diameter of its base is 7 cm. Two equal conical holes each of radius 3 cm and height 4 cm are cut off. Find the volume of the remaining solid.
Solution
The height of cylinder h = 15 cm
Radius of cylinder \[r = \frac{7}{2}\]
The volume of cylinder
`=pir^2h`
`=pi xx (7/2)^2 xx 15cm^2`
`=183.75 pi`
The radius of conical holes = 3 cm
Height of conical holes = 4 cm.
The volume of conical holes
`=1/3 pir^2h`
`=1/3pi xx 9 xx 4`
`=12 pi cm^3`
Clearly,
The volume of remaining solid
= vol. of cylinder − 2 × vol. of cone
\[= 183 . 75\pi - 24\pi\]
\[ = 501 . 6 {cm}^3\]
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