Subject: General Aptitude · Chapter: Area · Exam: 2009 · Marks: · Difficulty:
A square of area 40 sq. cm is inscribed in a circle as shown in the figure. The area (in sq.cm) of the semi-circle is $20 \pi$
(b)$25 \pi$
(c)$30 \pi$
(d)$40 \pi$
Answer
Answer (as printed): B
Explanation
Let each side of the square be $a$ cm and the radius of the semi-circle be $r$ cm. Then, $a^{2}=40 \mathrm{cm}^{2}$. $r^{2}=a^{2}+\left(\frac{a}{2}\right)^{2}=a^{2}+\frac{a^{2}}{4}=\frac{5 a^{2}}{4}=\left(\frac{5 \times 40}{4}\right)=50$. ∴ Area of the semi-circle $=\frac{\pi r^{2}}{2}=\left(\pi \times \frac{50}{2}\right) \mathrm{cm}^{2}-(25 \pi) \mathrm{cm}^{2}$.