What is the maximum area of a rectangle which can be inscribed in a circle of radius 2 cm?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → $8cm^2$
Use Circle Properties
The diagonal of the rectangle is the diameter of the circle.
Given: Radius $r=2 cm$ → Diameter $d=2r=4 cm$.
For a square, the relation between the side sss and the diagonal ddd is:
$s = \frac{d}{\sqrt{2}} = \frac{4}{\sqrt{2}} = 2\sqrt{2} \text{ cm}$
Compute the Area
$\text{Area} = s^2 = (2\sqrt{2})^2 = 4 \cdot 2 = 8 \text{ cm}^2$