Mensuration Ques 31
Question
If the circumference of a circle is $36 cm$ more than the perimeter of a square and the radius of the circle is $3 cm$ less than the side of the square. What is the measure of the area of square?(in sq. cm)
(1) 576
(2) 676
(3) 625
(4) 169
(5) 529
(IBPS SO (Agriculture) Exam, 29.01.2017)
Show Answer
Correct Answer: (1)
Solution: (1)
Let the side of the square be $x $ cm.
$\therefore$ Radius of circle $=(x-3) cm$
According to the question,
$2 \pi(x-3)-4 x=36$
$\Rightarrow 2 \pi x-6 \pi-4 x=36$
$\Rightarrow x(2 \pi-4)=36+6 \pi$
$\Rightarrow x\left(\frac{44}{7}-4\right)=36+\frac{6 \times 22}{7}$
$\Rightarrow x\left(\frac{44-28}{7}\right)=\frac{252+132}{7}$
$\Rightarrow 16 x=384$
$\Rightarrow x=\frac{384}{16}=24 cm$
$\therefore$ Area of square $=24 \times 24=576$ sq.cm.
BETA
