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 8?
(a)$\frac{133 \pi}{6}$ sq. m
(b)$121 \pi$ sq. m
(c)$132 \pi$ sq. m
(d)$\frac{176 \pi}{3}$ sq. m
Answer
Answer (as printed): D
Explanation
Area that can be grazed by the cow 385. Area that can be grazed by the cow = (Area of a circle with radius 8 cm ) - (Area of a sector = (Area of a circle with radius 8 cm ) - (Area of a sector with $r=8 \mathrm{m}$ and $\theta=30^{\circ}$ ) with $r=8 \mathrm{m}$ and $\theta=30^{\circ}$ ) $$\begin{aligned} & =\left(\pi \times 8^{2}-\pi \times 8^{2} \times \frac{30}{360}\right) \mathrm{m}^{2} \\ & =\left(64 \pi-\frac{64 \pi}{12}\right) \mathrm{m}^{2}=\left[64 \pi\left(1-\frac{1}{12}\right)\right] \mathrm{m}^{2} \\ & =\left(64 \pi \times \frac{11}{12}\right) \mathrm{m}^{2}=\frac{176 \pi}{3} \mathrm{m}^{2} . \end{aligned}$$