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The side of a square is $10 cm$ . Find the area between inscribed and circumscribed circles of the square.

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56 π c m^{2}

25 π c m^{2}

None of these

50 π c m^{2}

answer is A.

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Detailed Solution

Given that, side of the square is 10 cm
The side of the square is representing the diameter of inner circle so determine its radius

r_{1}

r 1 = 102

\Rightarrow

5
Determining the area of inner circle by using the formula for area of circle

A 1 = π r 12

A 1 = π 52

\Rightarrow

π

The diagonal of the square is representing the diameter of the outer circle d so determine the diagonal of the square by using

d = s i d e 2

d = 102

Determine the radius

r 2

of outer circle.

r 2 = 1022

⇒ 52

Using the radius

r_{2}

to determine the area of outer circle by using

A 2 = p r 22

A 2 = π 522

⇒

π

Determining the difference D between the area of inner and outer circle by subtracting the value of

A 1

from

A 2.

.
D =

50 π - 25 π

⇒

π

Therefore, area lies among the circle present at inner side of the square and circle present at outer side of the square is

25 π c m 2

.
Hence the correct option is 1.

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