Subject: General Aptitude · Chapter: Area · Exam: 2010 · Marks: · Difficulty:
The perimeter of a square is equal to twice the perimeter of a rectangle of length 8 cm and breadth 7 cm . What is the circumference of a semi-circle whose diameter is equal to the side of the square? (rounded off to two decimal places)
(a)23.57 cm
(b)38.57 cm
(c)42.46 cm
(d)47.47 cm
(e)None of these
Answer
Answer (as printed): A
Explanation
Perimeter of rectangle $=[2(8+7)] \mathrm{cm}=30 \mathrm{cm}$. Perimeter of square $=(2 \times 30) \mathrm{cm}=60 \mathrm{cm}$. Side of the square $=\left(\frac{60}{4}\right) \mathrm{cm}=15 \mathrm{cm}$. Radius of the semi-circle $=\left(\frac{15}{2}\right) \mathrm{cm}$. $$\text { ∴ } \text { Circumference }=\left(\frac{22}{7} \times \frac{15}{2}\right) \mathrm{cm}=\left(\frac{165}{7}\right) \mathrm{cm}=23.57 \mathrm{cm} .$$