The radius of a circle is equal to the diagonal of a square. If the area of the square is 32 sq units, then the area of the circle is:

Correct option is A

Given:

The radius of the circle is equal to the diagonal of a square.

The area of the square is 32 square units.

Formula Used:

Area of square =$$s^2$$

Area of circle = $$\pi r^2$$​​

Solution:

Let the side of the square be s.

​$$s^2$$​= 32 (given)

​$$s = \sqrt{32} = 4\sqrt{2} \, \text{units}$$​

The diagonal of the square can be calculated using the Pythagorean theorem. The diagonal d of a square with side s is:

d =$$\sqrt{s^2 + s^2} = \sqrt{2s^2} = s\sqrt{2}$$​​​

d = $$4\sqrt{2} \times \sqrt{2} = 4 \times 2 = 8 \, \text{units}$$​

Thus, the radius of the circle is 8 units.​

Area =$$\pi \times 8^2 = \pi \times 64 = 64\pi \, \text{square units}$$​​