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प्रश्न
If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of the cone hollowed out is ______.
पर्याय
1 : 1
1 : 3
2 : 1
3 : 1
MCQ
रिकाम्या जागा भरा
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उत्तर
If a cone of greatest possible volume is hollowed out from a solid wooden cylinder, then the ratio of the volume of remaining wood to the volume of the cone hollowed out is 2 : 1.
Explanation:
Volume of remaining wood = `"V"_"Cylinder" - "V"_"Cone"`
= `pir^2h - 1/3pir^2h`
= `2/3pir^2h`
Volume of hollowed out = `1/3pir^2h`
Required Ratio = `(2/3pir^2h)/(1/3pir^2h)`
= `2/3 xx 3/1`
= `2/1`
= 2 : 1
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