Question

A cow is tethered at point A by a rope. Neither the rope nor the cow is allowed to enter ∆ ABC.
∠ BAC = 30°
| (AB) = | (AC) = 10 m

What is the area that can be grazed by the cow if the length of the rope is 12 m?

• A. \( 133 \pi \, \frac{1}{6} \, \text{sq. m} \)
• B. \( 121 \pi \, \text{sq. m} \)
• C. \( 132 \pi \, \text{sq. m} \)
• D. \( \frac{176 \pi}{3} \, \text{sq. m} \)

Hint:

Ensure you correctly apply the formula for a sector area based on the rope length and the angle.

Answer 1

The Correct Option is A

For the second question, if the rope is 12 m long, the radius of the sector is now 12 m. Using the same formula for the area of a sector: \[ \text{Area of sector} = \frac{30^\circ}{360^\circ} \times \pi \times 12^2 = \frac{1}{12} \times \pi \times 144 = \frac{144 \pi}{12} = 12 \pi \, \text{sq. m}. \] Thus, the grazed area for the rope length of 12 m is \( 12 \pi \) square meters.