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From a wooden cylindrical block whose diameter is equal to its height a sphere of maximum possible volume is carved-out. Then what is the ratio of the volumes of the utilized wood to that of the wasted wood?

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2: 3

3: 2

3: 4

2: 1

answer is D.

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Detailed Solution

Given- a wooden cylindrical block whose diameter is equal to its height.
Height of sphere of maximum possible volume will be h = 2r.

Volume of wooden cylinder block = π r 2 h = π r 2 (2 r) = 2 π r 3

Volume of utilized wood = volume of sphere =

43 π r 3

Volume of wasted wood = 2 π r 3 − 43 π r 3 = 23 π r 3

So, the ratio of the volumes of the utilized wood to that of the wasted wood is,

43 π r 3 23 π r 3 = 42 = 21 = 2 : 1

Thus, the ratio is 2: 1. Hence, option 4 is the correct option.

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