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

Answer 1

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.