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What will be the area of the largest square that can be cut out of a circle of radius 10 cm?

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100

cm 2

200

cm 2

300

cm 2

400

cm 2

answer is B.

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Detailed Solution

We need to find the area of the largest square that can be cut out of a circle of radius 10 cm. Question Image

Now, if we observe the above diagram,
So, the diagonal of the square is BD =Diameter of circle = 10 cm.
Now, if we consider the right-angled triangle ABD,
Let AD = AB =

x

. So, applying the Pythagoras theorem on this triangle, we get,

A D 2 + A B 2 = B D 2 x 2 + x 2 = 202 2 x 2 = 400 x 2 = 4002 x 2 = 200............. (i)

Now, as the side of the square is given as

x

, so its area will be

x 2

.
So, from the equation (i), we have the area of the largest square as 200

m 2

.
Hence, the correct option is (2).

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