Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
What is the area that can be grazed by the cow if the length of the rope is 12 m ?
(a)$134 \frac{1}{3} \pi$ sq. m
(b)$121 \pi$ sq.m
(c)$132 \pi$ sq.m
(d)$\frac{176 \pi}{3}$ sq. m
Answer
Answer (as printed): A
Explanation
In $\triangle A B C, A B=A C \Rightarrow \angle A B C=\angle A C B=75^{\circ}$. So, $\angle C B D=\angle B C E=\left(180^{\circ}-75^{\circ}\right)=105^{\circ}$. $B D=C E=2 \mathrm{m}$. ∴ Area that can be grazed by the cow = [Area of a circle with radius 12 cm - Area of a sector with $r=12 \mathrm{m}$ and $\theta=30^{\circ}$ ] $+2 \times$ (Area of a sector with $r=2 \mathrm{m}$ and $\theta=105^{\circ}$ ) $=\left[\left\{\pi \times(12)^{2}-\pi \times(12)^{2} \times \frac{30}{360}\right\}+2\left(\pi \times 2^{2} \times \frac{105}{360}\right)\right] \mathrm{m}^{2}$ $=\left[(144 \pi-12 \pi)+\frac{7}{3} \pi\right] \mathrm{m}^{2}$ $=\left[\left(132+2 \frac{1}{3}\right) \pi\right] \mathrm{m}^{2}=\left(134 \frac{1}{3} \pi\right) \mathrm{m}^{2}$.