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CAT 1998 — QA Question 12

Basics of Mensuration/PrismEasy
Passage / Data

Answer the next 2 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 12 m?

Answer & solution

  • 133π 13 sq.m

  • B

    121π sq.m

  • C

    132π sq.m

  • D

    176π3 sq.m

Solution

If the length of the rope is 12 m, then the total area that can be grazed by the cow is as depicted in the diagram.

Area 1 is (the area of the circle with radius 12) – (Area of the sector of the same circle with angle 30º)

So area 1 = π(12)² - 30360π(12)² = 132π

Since the length of the rope is higher than the sides of the triangle (viz. AB and AC), if the cow reaches point B or C, there would still be a part of the rope (12 – 10) = 2 m in length. With this extra length available the cow can further graze an area equivalent to some part of the circle with radius = 2 m from both points, i.e. B and C. This is depicted as area 2 and area 3 in the diagram. Hence, the actual area grazed will be slightly more than 132π . The only answer choice that supports this is (a).

CAT 1998 QA Q12: What is the area that can be grazed by the cow if the length of the rope is 12 m? — Solution | TheCATExam