The small square is $100 sq . cm$ . The area of the large square is $sq . cm$ is :

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144 c m^{2}

165 c m^{2}

200 c m^{2}

400 c m^{2}

answer is C.

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Detailed Solution

Concept- The concepts of geometry are used. The theorems and rules related to the circle are prominently applied here in this question.
We know that the formula to find the area of a square can be expressed as

l^{2}

where

l

is the length of a square. Hence, the value of

l

\sqrt{100} \Rightarrow 10 cm

Then, we will find the diagonal of the square using the formula

\sqrt{2} l

, if

l

is the length of the square. Here, length we found out as

10 cm

. The length of diagonal is

10 \sqrt{2} cm

Here, there is a property that, the length of diagonal of inscribed square and the diameter of circle is equal in length.
Diameter of the circle is

10 \sqrt{2} cm

.
Now, we will consider the circle and square only, so here, we will use the property that, length of the diameter of the circle equals the length of the side of the square.
The length of the side of the square will be