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A circle is inscribed in a square of side $14 m$ . The ratio of the area of the circle and that of the square is,

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3.14:2

4:5

153.93 : 196

answer is C.

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Detailed Solution

It is given that a circle is inscribed in a square of side

14 m

. We need to find the ratio of the area of the circle and that of the square.
We know that when a circle is inscribed in a square, the diameter of the circle is equal to the side of the square.
By data,

Side of square = 14 m

\Rightarrow Diameter of circle = Side of square

\Rightarrow Diameter of circle = 14 m

\Rightarrow Radis of circle = \frac{Diameter of circle}{2}

\Rightarrow Radis of circle = \frac{14}{2}

\Rightarrow Radis of circle = 7 m

We know that,

Area of square = a^{2}

, where

a

is its side.

\Rightarrow Area of square = (14)^{2}

\Rightarrow Area of square = 196 m^{2}

We know that,

Area of circle = п r^{2}

, where

r

is the radius of the circle.

\Rightarrow Area of circle = п (7)^{2}

\Rightarrow Area of circle = 3.14 \times 49

\Rightarrow Area of circle = 153.93 m^{2}

Therefore,

\frac{Area of circle}{Area of square} = \frac{153.93 m^{2}}{196 m^{2}}

\Rightarrow \frac{Area of circle}{Area of square} = 153.93 : 196

Therefore, the ratio of the area of the circle and that of the square is

153.93 : 196

.
Hence, the correct option is 3.

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