The area of a square is 100 cm 2 . The circumference (in cm) of the largest circle cut of it is:

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The area of a square is 100 $cm 2$ . The circumference (in cm) of the largest circle cut of it is:

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5 π

10 π

15 π

20 π

answer is B.

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Detailed Solution

Given, the area of a square is 100

cm 2

Now, the area of a square with side length say ‘a’ is the square of its side length i.e.,

a 2

.
So, we can determine its side length using the formula for its area as follows,
Question Image

Now, we can conclude from the figure above that the diameter of the largest circle will be nothing but the side length of the square, i.e., the diameter = 10 cm.
So, its radius will be the half of the diameter i.e.,

102 = 5

cm.
Now, we know that the perimeter of a circle with radius ‘r’ is given as

2 π r

.
So, the perimeter of the largest circle is,

=2 π r =2 × π × 5 =10 π cm

So, the perimeter of the largest circle which can be cut from the square is obtained as

10 π cm

.
Hence, the correct option is (2).

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