A square pond has 2m sides and is 1m deep. If it is to be enlarged, the depth remaining the same, into a circular pond with the diagonal of the square as diameter as shown in the figure, then what would be the volume of earth to be removed?

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Q: 138 (IAS/1998)
A square pond has 2m sides and is 1m deep. If it is to be enlarged, the depth remaining the same, into a circular pond with the diagonal of the square as diameter as shown in the figure, then what would be the volume of earth to be removed?

question_subject: 

Maths

question_exam: 

IAS

stats: 

0,1,6,1,3,3,0

keywords: 

{'circular pond': [0, 1, 0, 0], 'square pond': [0, 1, 0, 0], 'volume': [0, 0, 1, 0], 'diameter': [0, 3, 3, 4], 'square': [0, 0, 0, 1], 'depth': [0, 0, 0, 1], 'earth': [0, 1, 1, 1], 'diagonal': [0, 1, 0, 0], 'figure': [0, 1, 1, 0], 'm3': [1, 2, 2, 1]}

The question is asking for the difference between the volume of a new circular pond and the volume of the original square pond. The size of the circular pond is based on the diagonal of the square pond. Given that the side length of the square is 2m, by using Pythagorean theorem, the diagonal (d) = √(2² + 2²) = √8 = 2√2m. The diameter of the new circular pond will be 2√2m.

Volume of square pond = side^3 = 2^3 = 8m³.

Volume of circular pond = pi*(d/2)²*depth = pi*(2√2/2)²*1 = 2pi m³.

Therefore, earth to be removed = Volume of circular pond - Volume of square pond = 2pi - 8 m³ = (2*pi-4)m3

Option 1 is correct.

Options 2, 3 and 4 aren`t correct as they don`t correctly represent the difference in volumes between the two ponds. Option 2 subtracts 4 from 4pi, Option 3 subtracts 2 from 4pi and Option 4 subtracts