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A square park has each side of $100$ m. At each corner of the park, there is a flower bed in the form of a quadrant of radius 14 m as shown in the figure below.

Find the area of the remaining part of the park.

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154 m^{2}

9866 m^{2}

9384 m^{2}

152 m^{2}

answer is C.

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Detailed Solution

Given that side of square park is 100m, radius of quadrant is 14m.
Question Image

Length of the side of the park

= 100 m

So, area of park

= 100 \times 100

10000 m^{2}

Radius of each quadrant circle =14m
Area of each quadrant circle =

\frac{1}{4} \times π \times r^{2}

\Rightarrow \frac{1}{4} \times π \times {(14)}^{2}

\Rightarrow \frac{1}{4} \times \frac{22}{7} \times 14 \times 14

\Rightarrow 11 \times 14

\Rightarrow 154 m^{2}

Area of remaining part = Area of park –

4 \times

Area of quadrant of circle

\Rightarrow 10000 - 4 \times 154

\Rightarrow 9384 m^{2}

Thus, area of remaining part =

9384 m^{2}

Therefore, option (3) is correct.

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