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.]

Question: 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.]

Solution:
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 = (22/7) × 19² sq. m.
When the length of the rope is increased to 30 m, grazing area becomes = (22/7) × 30² sq. m.
The additional area it could graze when length is increased from 19 m to 30 m = (22/7) × (30² - 19²) sq. m.
= (22/7) × (30 + 19)(30 - 19) = (22/7) × 49 × 11 = 1694 sq. m.