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If the perimeter of a circle is equal to that of a square, then the ratio of their areas is (A) \[22:7\] (B) \[14:11\] (C) \[7:22\] (D) \[11:14\]
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is (A) \[22:7\] (B) \[14:11\] (C) \[7:22\] (D) \[11:14\]
Areas Related to Circles | Exercise 11.1 | Maths | NCERT Exemplar
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is (A) \[22:7\] (B) \[14:11\] (C) \[7:22\] (D) \[11:14\]

The correct option is (B) \[14:11\]

Explanation:

Let us take r as the radius of the circle and a as the side of the square.

From the given question,

Perimeter of a circle of radius r = Perimeter of a square of side a

i.e., \[2\pi r=4a\]

we got  \[a=\pi r/2\]

Area of the circle of radius r  = \[{{r}^{2}}\] and Area of the square of side a = \[{{a}^{2}}\]

Now, Ratio of their areas is equal to (Area of circle)/(Area of square)

\[=\frac{\pi {{r}^{2}}}{{{a}^{2}}}=\frac{\pi {{r}^{2}}}{{{\left( \frac{\pi {{r}^{2}}}{2} \right)}^{2}}}=\frac{\pi {{r}^{2}}}{\frac{{{\pi }^{2}}{{r}^{2}}}{4}}\]

= \[4\pi \]

= \[[4/(22/7)]\]

= \[14/11\]

Therefore, Option B is correct.

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