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Q.

The circumference of a circle is $50 cm$ . What will be the side of a square that can be inscribed in the circle?

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a

25 π

b

\frac{25 \sqrt{2}}{π}

c

22 π

d

\frac{25}{π}

answer is A.

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Detailed Solution

Given that, Circumference of the circle is 50 cm.
Determine the radius of the circle by using its circumference.

2 π r = 50

Solve the equation for r.

r = 50 2 π

⇒ r = 25 π

Determine the diameter D of the circle by multiplying the value of r by 2.

D = 50 π

The diameter D of the circle represents the diagonal of the square.
Determine the side S of the square that can be inserted into the circle by using

D = S 2

.

50 π = S 2

⇒ S = 252 π

Therefore, side of the square present in the circle

252 π

cm.
Hence the correct option is 1.

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The circumference of a circle is 50 cm . What will be the side of a square that can be inscribed in the circle?