Question

The area of the square that can be inscribed in a circle of radius 8 cm is ______.

Options

• 256 cm² 

• 128 cm² 

• `64sqrt(2)` cm² 

• 64 cm² 

Answer 1

The area of the square that can be inscribed in a circle of radius 8 cm is 128 cm².

Explanation:

Given, radius of circle, r = OC = 8cm.

∴ Diameter of the circle = AC = 2 × OC = 2 × 8 = 16 cm

Which is equal to the diagonal of a square.

Let side of square be x.

In right-angled ΔABC,

AC² = AB² + BC²   ......[By Pythagoras theorem]

⇒ `(16)^2 = x^2 + x^2`

⇒ 256 = `x^2 + x^2`

⇒ `x^2 = 128`

∴ Area of square = `x^2 = 128  cm^2`

Alternative Method:

Radius of circle (r) = 8 cm

Diameter of circle (d) = 2r = 2 × 8 = 16 cm

Since, square inscribed in circle.

∴ Diagonal of the square = Diameter of circle

Now, Area of square = `("Diagonals")^2/2`

= `(16)^2/2`

= `256/2`

= 128 cm²