This GMAT Math practice question is a Solid Geometry (Mensuration) question: Concept: Area of circle.
Question 14: The length of a rope, to which a cow is tied, is increased from 19 m to 30 m. How much additional ground will it be able to graze? Assume that the cow is able to move on all sides with equal ease. Use π = 227 in your calculations.
The cow can graze the area covered by the circle of radius 19 m initially, because the length of the rope is 19 m.
Area of a circle = π × (radius)2
Therefore, the initial area that the cow can graze = 227 × 192 sq m.
When the length of the rope is increased to 30 m, grazing area becomes = 227 * 302 sq m.
The additional area it could graze when length is increased from 19 m to 30 m = 227 × (302 - 192) sq m.
227 × (30 + 19)(30 - 19) = 227 × 49 × 11 = 1694 sq m.
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