If a circle has a radius of 4 cm then the area of the largest square that would fit inside the circle would be ____________.

Correct option is D

Given:

Radius of the circle  r = 4 cm

The largest square that fits inside the circle will have its diagonal equal to the diameter of the circle.

Formula Used:

The diagonal d of the square is equal to the diameter of the circle:

d=2r

The relation between the side s of a square and its diagonal is:

d =$$s\sqrt{2}$$​​

The area of the square is:

A = $$s^2$$​​

Solution:

2r = $$s\sqrt{2}$$​​

2(4) = $$s\sqrt{2}$$​​

8 = $$s\sqrt{2}$$​​

s = $$\frac{8}{\sqrt{2}}$$​ =$$\frac{8\sqrt{2}}{2} = 4\sqrt{2}$$​​

A =$$(4\sqrt{2})^2$$​​

A = $$16 \times 2 = 32 \text{ cm}^2$$

Option (D) is right.