GMAT Quant Questions | Geometry #14

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 = \\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

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Video Explanation

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Explanatory Answer | GMAT Geometry

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 = \\frac{22}{7}) × 19² sq m.

When the length of the rope is increased to 30 m, grazing area becomes = \\frac{22}{7}) * 30² sq m.

The additional area it could graze when length is increased from 19 m to 30 m = \\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.