Question

The maximum area of a rectangle that can be inscribed in a circle of radius $2$ units is (in square units).

• A. $4$
• B. $8\pi$
• C. $8$
• D. $5$

Answer 1

Answer: (C)

$8$

The sides of a rectangle are, $2rsin\theta$ and $2rcos\theta$ .

Area $=4r^{2}sin\theta cos\theta$

$=2r^{2}sin2\theta$

For maximum value, $sin2\theta =90$,

Max area $=2r^2$

$=2\times 4$

$=8$

(c)