Mensuration Ques 15
Question
The circumference of a semicircle of area 1925 sq. cm is equal to the breadth of a rectangle. If the length of the rectangle is equal to the perimeter of a square of side $48 cm$. What is the perimeter of the rectangle?
(1) $734 cm$
(2) $754 cm$
(3) $745 cm$
(4) Cannot be determined
(5) None of these
(UCO Bank PO Exam. 30.01.2011)
Show Answer
Correct Answer: (5)
Solution: (5)
$\frac{\pi r^{2}}{2}=1925$
$\Rightarrow \pi r^{2}=1925 \times 2$
$\Rightarrow \frac{22}{7} \times r^{2}=1925 \times 2$
$\Rightarrow r^{2}=\frac{1925 \times 2 \times 7}{22}=1225$
$\therefore r=\sqrt{1225}=35$
$\therefore$ Breadth of rectangle $=\pi r+2 r$
$=(\pi+2) r=\left(\frac{22}{7}+2\right) \times 35$
$=\left(\frac{22+14}{7}\right) \times 35=\frac{36}{7} \times 35$
$=180 cm$
Length of rectangle $=$ Perimeter of square $=4 \times 48=192 cm$
$\therefore$ Perimeter of rectangle $=2$ (length + breadth)
$=2(192+180)$
$=744 cm$
BETA
