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Question
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is ______.
Options
22 : 7
13 : 22
14 : 11
7 : 22
22 : 13
11 : 14
Solution
If the perimeter of a circle is equal to that of a square, then the ratio of their areas is 14 : 11.
Explanation:
Let radius of circle be r and side of a square be a.
According to the given condition,
Perimeter of a circle = Perimeter of a square
∴ 2πr = 4a
⇒ a = `(π"r")/2` ...(i)
Now, `"Area of circle"/"Area of square"`
= `(π"r"^2)/("a")^2`
= `(π"r"^2)/((π"r")/2)^2` ...[From equation (i)]
= `(π"r"^2)/((π^2"r"^2)/4)`
= `4/π`
= `4/(22/7)`
= `28/22`
= `14/11`
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