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Question
The area of a square is 100 cm2. The circumference (in cm) of the largest circle cut of it is ______.
Options
5 π
10 π
15 π
20 π
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Solution
The area of a square is 100 cm2. The circumference (in cm) of the largest circle cut of it is 10 π.
Explanation:
Let the side of square be a cm.
Given, area of square = 100 cm2
∴ Area of square = a2
⇒ a2 = 100 cm2 ...[∵ Area of square = (Side)2]
⇒ a = `sqrt(100)`
⇒ a = 10 cm
Now, for the largest circle in the square, diameter of the circle must be equal to the side of square.
∴ Diameter = Side of a square = 10 cm
⇒ 2r = 10 cm ...[∵ Diameter = 2 × radius]
⇒ r = 5 cm
∴ Circumference of the circle = 2 πr = 2 × π × 5 = 10 π cm.
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