Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
Between a square of perimeter 44 cm and a circle of circumference 44 cm, which figure has larger area and by how much?
(a)Both have equal area
(b)Square, $33 \mathrm{cm}^{2}$
(c)Circle, $33 \mathrm{cm}^{2}$
(d)Square, $495 \mathrm{cm}^{2}$
Answer
Answer (as printed): C
Explanation
Side of the square $=\frac{44}{4} \mathrm{cm}=11 \mathrm{cm}$. Area of the square $=(11 \times 11) \mathrm{cm}^{2}=121 \mathrm{cm}^{2}$. $$2 \pi R=44 \Leftrightarrow 2 \times \frac{22}{7} \times R=44 \Leftrightarrow R=7 \mathrm{cm} .$$ Area of circle $=\pi R^{2}=\left(\frac{22}{7} \times 7 \times 7\right) \mathrm{cm}^{2}=154 \mathrm{cm}^{2}$. ∴ Area of the circle is larger by $33 \mathrm{cm}^{2}$.