The radius of a cone is √2 times the height of the cone. A cube of maximum possible volume is cut from the same cone. What is the ratio of the volume of the cone to the volume of the cube?
3.18π
2.35π
2.35
Can't be determined
A
3.18π
B
2.35
C
Can't be determined
D
2.35π
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Solution
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Let height of cone be 'h'. Then its radius r=√2h
Volume of cone =13πr2h=2√2πh33
Let side of cube be x, then top of cone has the size (h−x) and radius x2 using similar triangle property.
x2h−x=√2hh⇒x=2√2h2√2+1
Volume of cube =(2√2h2√2+1)3
∴ Required ratio =2√2h33(2√2h2√2+1)3=π×(2√2+1)324=2.35π
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