The radius of a cone is root 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?
Answers
Answer:
Refer to the picture first.
In the given figure, you can see that
Now , BC = x / √2
Therefore, √2 ( h-x)/x = h/(√2 h) = 1/√2
2 h-2 x = x
Hence, 3 x = 2 h
Now, Volume of cone/ Volume of cube = 1/3 π (2h)³/ (2h)³
So, (1/3 π 8h³)/ 8h³ = 9/4π = 99/14
Hence, the ratio of volume of cone to the volume of the cube is 99/14.
Answer:
Step-by-step explanation:
Refer to the picture first.
In the given figure, you can see that
Now , BC = x / √2
Therefore, √2 ( h-x)/x = h/(√2 h) = 1/√2
2 h-2 x = x
Hence, 3 x = 2 h
Now, Volume of cone/ Volume of cube = 1/3 π (2h)³/ (2h)³
So, (1/3 π 8h³)/ 8h³ = 9/4π = 99/14
Hence, the ratio of volume of cone to the volume of the cube is 99/14.
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