The area of a quadrant of a circle whose circumference is $616 cm$ will be

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7546 c m^{2}

7500 c m^{2}

7552 c m^{2}

None of these

answer is A.

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Detailed Solution

Given that, circumference of circle is

616 cm

.
Determine the radius of the circle by using the circumference.

2 πr = 616

\Rightarrow 2 \times \frac{22}{7} \times r = 616

\Rightarrow r = \frac{615 \times 7}{44}

\Rightarrow r = 98

Determine the area of quadrant of the circle by using

A = \frac{π r^{2}}{4}

A = \frac{22 \times 98^{2}}{7 \times 4}

\Rightarrow A = 7546

Therefore, area of the quadrant of the circle is represented by 7546 cm

2

.
Hence the correct option is 1.

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