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If the circumference of a circle is increased by $50 %$ then its area will be increased by

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100 %

125 %

150 %

75 %

answer is B.

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Detailed Solution

Given that the circumference of a circle is increased by

50 %

.
We have to find the increase percentage in the area of the circle.
The area of a circle can be expressed as

A = π r 2

. Here r is the radius of the circle.
Suppose the initial and new radius be

r 1

and

r 2

. Since the circumference of a circle is increased by

50 %

.
So, let the initial circumference is

100 %

, and the new circumference is,

150 %

.
Thus,

C 2 C 1 = 2 π r 2 2 π r 1 ⇒ 2 π r 2 2 π r 1 = 150100 ⇒ r 2 r 1 = 32

Now, the ratio of the area of the circles is,

A 2 A 1 = π r 2 2 π r 1 2 ⇒ A 2 A 1 = 322 ⇒ A 2 A 1 = 94

Thus, increase in the area,

A d

is,

A_{d} = \frac{increased area}{original area} \times 100

\Rightarrow A_{d} = \frac{(\frac{9}{4} - 1)}{1} \times 100

\Rightarrow A_{d} = \frac{5}{4} \times 100

\Rightarrow A_{d} = 125 %

The increased percentage in the area of the circle is 125%.
Therefore, the correct option is 2.

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