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प्रश्न
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is ______.
रिक्त स्थान भरें
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उत्तर
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is 14 : 11.
Explanation:
Let circle radius = r and square side = a.
Equal perimeters give 2πr = 4a ⇒ `a = (πr)/2`.
Area ratio (circle : square) = `(πr^2)/a^2`
= `(πr^2)/((π^2r^2)/4)`
= `4/π`
Using `π = 22/7`,
`4/π = 4/(22/7)`
= `28/22`
= `14/11`
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