Mensuration Ques 25
Question
The difference between the area of circular field and the area of a square field is $168 sq$. $m$. Side of the square field is equal to the diameter of the circular field. What is the cost of fencing the square field at the rate of Rs. 20 per metre?(in Rs.)
(1) 2480
(2) 2420
(3) 2520
(4) 2240
(5) 2340
(Bank of Maharashtra PO Exam, 26.10.2016)
Show Answer
Correct Answer: (4)
Solution: (4)
Side of square field $=2 x$ metre (Let)
$\therefore$ Radius of circular field $=x$ metre
According to the question,
$4 x^{2}-\pi x^{2}=168$
$\Rightarrow x^{2}(4-\pi)=168$
$\Rightarrow x^{2}\left(4-\frac{22}{7}\right)=168$
$\Rightarrow x^{2}\left(\frac{28-22}{7}\right)=168$
$\Rightarrow x^{2} \times \frac{6}{7}=168$
$\Rightarrow x^{2}=\frac{168 \times 7}{6}=196$
$\Rightarrow x=\sqrt{196}=14$ metre
$\therefore$ Perimeter of square field $=4 \times$ side
$=4 \times 2 x=8 x$ metre
$=8 \times 14=112$ metre
$\therefore$ Total cost of fencing $=$ Rs. $(112 \times 20)=$ Rs. 2240
BETA
