The GMAT Sample Math question for the day is from the topic Mensuration.

Question
The length of a rope, to which a cow is tied, is increased from 19m to 30m. How much additional ground will it be able to graze? Assume that the cow is able to move on all sides with equal ease.

A. 1696 sq m
B. 1694 sq m
C. 1594 sq m
D. 1756 sq.m
E. 1896 sq.m

The correct choice is (B) and the correct answer is 1694 sq m.

Explanatory Answer
The cow can graze the area covered by the circle of radius 19m initially, as the length of the rope is 19m.

Therefore, the grazing area=(22/7)*19² sq m.

Note: Area of a circle = Pi * (radius)², where Pi = (22/7)

When the length of the rope is increased to 30 m, grazing area becomes = (22/7) * 30² sq m.

Therefore, the additional area it could graze when length is increased from 19m to 30m
= 22/7*(30²- 19²) sq m.

It can be simplified as (22/7)*(30+ 19)(30 –19)=(22/7)*49*11 = 1694 sq m.

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