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Question

From a wooden cylindrical block whose diameter is equal to its height a sphere of maximum possible volume is carved out What is the ratio of the volume of the utilised wood to that of the wasted wood?

A
2:1
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B
1:2
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C
2:3
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D
3:2
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Solution

The correct option is A 2:1
Given a wooden cylindrical block whose diameter is equal to its height H=2r
Then volume of wooden cylindrical block=π(r)2×2r=2πr3
The volume of utilized wood =volume of sphere=43πr3
Then volume of wasted wood =2πr343πr3=23πr3
So required ratio=42πr3:23πr3=2:1

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