A wire of length 6 m is stretched such that its radius is reduced by 20 Which one of the following i...........

Quantitative Aptitude( Paper-I ) Mensuration 2D

A wire of length 6 m is stretched such that its radius is reduced by 20%. Which one of the following is the value of increase in its length ?

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CAPF 2020 Paper-1

50%

56.25%

62.25%

75%

- Initially, the volume of the wire is constant as it stretches. The volume \( V = \pi r^2 L \).

- Given that the radius is reduced by 20%, new radius \( r' = 0.8r \).

- Since the volume remains constant, \( \pi r^2 L = \pi (0.8r)^2 L' \).

- Simplifying, \( L/L' = (0.8)^2 \).

- So, \( L' = L/(0.8^2) = L/0.64 = 1.5625L \).

- The new length is 156.25% of the original, an increase of 56.25%.

- Comparing options, Option 2 indicates a 56.25% increase, which aligns with the calculations.

The correct answer is Option 2: 56.25%.

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