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Question
What will be the area of the largest square that can be cut out of a circle of radius 10 cm?
Options
100 cm2
200 cm2
300 cm2
400 cm2
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Solution
200 cm2
Explanation:
Given, radius of circle = 10 cm
The largest square that can be cut out of a circle of radius 10 cm will have its diagonal equal to the diameter of the circle.
Let the side of a square be x
Then, area of the square = x × x = x2 cm2 ...[∵ Area of square = (Side)2]
Now, In right-angled ΔDAB,
(BD)2 = (AD)2 + (AB)2 ...[By Pythagoras theorem]
∵ (20)2 = x2 + x2 ...[∵ Diagonal and diameter = 2 × radius = 2 × 10 = 20 cm]
⇒ 2x2 = 400
⇒ x2 = 200
∴ (Side)2 = 200
Hence, the area of the largest square is 200 cm2.
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