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Q.

Find the area of a quadrant of a circle whose circumference is 22 cm.

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a

9.625

{cm}^{2}

b

8.625

{cm}^{2}

c

7.625

{cm}^{2}

d

6.625

{cm}^{2}

answer is A.

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Detailed Solution

Concept- The coordinate system's two axes, the x-axis and the y-axis, constitute a region called a quadrant. The quadrants are generated when the two axes, the x-axis and the y-axis, cross at a 90-degree angle. These areas include coordinates, or positive and negative values of the x- and y-axes.
To start, calculate the circle's radius using the circumference of the circle formula 2r. Since the quadrant of a circle is the fourteenth of the circle, divide the formula for the area of the circle

\frac{1}{4} th

to obtain the area of the quadrant.
Given that the circle's circumference is 22 cm. The circumference of a circle with radius "r" is equal to 2πr.

π = \frac{22}{7}

2

πr

=22

r = \frac{22}{2 π} = \frac{22 \times 7}{2 \times 22} = 3.5 cm

Area of a circle's quadrant

= \frac{Area of the circle}{4} = \frac{π r^{2}}{4} = \frac{22 \times {(3.5)}^{2}}{7 \times 4} = 9.625 {cm}^{2}

Hence, the correct answer is option 1) 9.625

{cm}^{2}

.

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