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CAT 1998 — QA Question 11

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 8 m?

Answer & solution

  • A

    134π 13 sq.m

  • B

    121π sq.m

  • C

    132π sq.m

  • 176π3 sq.m

Solution

It can be seen that if the length of the rope is 8 m, then the cow will be able to graze an area equal to (the area of the circle with radius 8m) – (Area of the sector of the same circle with angle 30°) = π(8)² - 30360π(8)2

= 64π - 112 (64π) = 64π (1112) = 176π3 sq.m

Shortcut:
Area grazed without restriction is 64π m2 it should  be less than 64π sq.m. with restriction. So choice (d).

CAT 1998 QA Q11: What is the area that can be grazed by the cow if the length of the rope is 8 m? — Solution | TheCATExam