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Question
A hemispherical and a conical hole is scooped out of a.solid wooden cylinder. Find the volume of the remaining solid where the measurements are as follows:
The height of the solid cylinder is 7 cm, radius of each of hemisphere, cone and cylinder is 3 cm. Height of cone is 3 cm.
Give your answer correct to the nearest whole number.Taken`pi = 22/7`.
Solution
Required volume = Volume of cylinder – Volume of hemisphere – Volume of Cone ...(1)
For cone = Volume `= 1/3 pi r_1^2 h-1`
`= 1/3 xx pi xx(3)^2 xx 3`
`= 9 pi " cm"^3` ...(2)
For Hemisphere = Volume ` = 2/3 pi r _ 2^3 `
` = 2/3 xx pi xx (3)^3`
`= 18 pi " cm"^3 ` ...(3)
For cylinder = Volume `= pi r _3^2 h _3`
` = pi xx (3)^2 xx 7`
` = 63 pi` ...(4)
∴ Required volume = 63π - 18π - 9π {From (1), (2), (3) and (4)}
= 36 π
`= 36 xx 22/7 " cm"^3`
` = 113.14 " cm"^3`
` = 113 " cm"^3`
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