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

Answer 1

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.