GMAT Quant Practice : Area of circles

Concept: Area of circle.

This GMAT Math practice question is a Solid Geometry (Mensuration) question: Concept: Area of circle.

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. Use π = \\frac{22}{7}\\) in your calculations.

  1. 1696 sq m
  2. 1694 sq m
  3. 1594 sq m
  4. 1756 sq.m
  5. 1896 sq.m

Explanatory Answer

Video explanation will be added soon

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

Area of a circle = π * (radius)2
Therefore, the initial area that the cow can graze = \\frac{22}{7}\\) * 192 sq m.

When the length of the rope is increased to 30m, grazing area becomes = \\frac{22}{7}\\) * 302 sq m.
The additional area it could graze when length is increased from 19m to 30m

= \\frac{22}{7}\\) * (302 - 192) sq m.
\\frac{22}{7}\\) * (30 + 19)(30 - 19) = \\frac{22}{7} \\) * 49 * 11 = 1694 sq m.

Choice B is the correct answer.

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