Question

A cow is tethered to an external corner of a rectangular barn measuring 20m by 35m. If the cow's rope is 30m long, what is the re, in square meters, which the cow can graze?Note: the barn door is closed; the cow cannot get into the barn.

Answer 1

The area which the cow can graze is 2199.115 m²

Explanation:

Here we have;

Size of barn = 20 m by 35 m

Length of the cow's rope = 30 m

The cow, can graze an area given by a circle of radius equal to the length of the cows rope less the segment where the barn is located hence, we have;

The length of the barn > The length of the cow's rope

The width of the barn < The width of the cow's rope, therefore, the cow can graze approximately 3/4 of the circle of radius 30 m which is 3/4×π×30² = 2120.575 m²

The cow can also graze on the adjacent side of the barn after crossing the width of the barn in an area of 1/4×π×(30 - 20)² = 78.54 m²

Hence the total area the cow can graze while the cow is tethered to the external corner of the rectangular barn = 2120.575 m² + 78.54 m² = 2199.115 m².