Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If a wire is bent into the shape of a square, then the area of the square is 81 sq. cm. When the wire is bent into a semi-circular shape, then the area of the semi-circle will be
(a)$22 \mathrm{cm}^{2}$
(b)$44 \mathrm{cm}^{2}$
(c)$77 \mathrm{cm}^{2}$
(d)$154 \mathrm{cm}^{2}$
Answer
Answer (as printed): C
Explanation
Length of each side of the square $=\sqrt{81} \mathrm{cm}=9 \mathrm{cm}$. Length of wire $=(9 \times 4) \mathrm{cm}=36 \mathrm{cm}$. $$\pi R+2 R=36 \Leftrightarrow(\pi+2) R=36 \Leftrightarrow R=\frac{36}{\left(\frac{22}{7}+2\right)}=7 \mathrm{cm} .$$ Area of the semicircle $$=\frac{1}{2} \pi R^{2}=\left(\frac{1}{2} \times \frac{22}{7} \times 7 \times 7\right) \mathrm{cm}^{2}=77 \mathrm{cm}^{2} .$$