Answer the questions based on the following information. A cow is tethered at point A by a rope. Neither the rope nor the cow is allowed to enter ΔABC.
∠BAC = 30°
I(AB) = I(AC) = 10 m
What is the area that can be grazed by the cow if the length of the rope is 8 m?
Solution
Area grazed by cow will be = (circle passing through P and Q) - (Area of circle inside the triangle)
= $$\pi r^2 - \frac{\pi r^2}{12}$$ = $$\frac{176\pi}{3}$$
Hi, the area of the sector is $$\frac{30}{360}\pi\ r^2$$ this is the area where the cow can't grace. So, we have to subtract it from total area of circle.
Hi Sanjana. We cannot do that, as the rest of the area of the circle is not relevant to the triangle. We find out the area of the segment by dividing the total area by 12, as the angle is given as 30$$^{\circ\ }$$. Since the total angle for a circle is 360, we get the area of the sector by dividing the total by 12, as 12 times 30 is 360. Hope this helps.
how we got the value of pie r^2/ 12 ???????............................................................................................................................................................................................................................................................................
Hi Ashish Patel, Area of the sector of a circle = $$\frac{\theta}{360}\times\ \pi\ r^2$$ It is given, $$\theta=30^{\circ\ }$$ Area = $$\frac{30}{360}\times\ \pi\ r^2$$ = $$\ \frac{\ \pi\ r^2}{12}$$ Hope this helps!