If diameter of a circle is increased by $40 %$ . Then, by how much percent will its area increase?

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90%

80%

96%

85%

answer is C.

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Detailed Solution

Given that the diameter of a circle is increased by

40 % .

We have the following formulae,
Diameter of a circle

= 2 r

Area of a circle =

π r 2

The new diameter will be,

= d + 0.4 d = 1.4 d

The new radius will be,

= r + 0.4 r = 75 r

The new area will be,

= π 7 r 5 2 = π 49 r 2 25 .

The increase in the area will be,

= 49 π r 2 25 − π r 2 = 2425 π r 2

The percentage increase will be,

= 24 / 25 π r 2 π r 2 × 100 = 2425 × 100 = 96 %

Thus, the percentage increase is 96 %.
Therefore the correct option is 3.

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