Question

A goat is tied to the corner of a rectangular shed in a large field full of grass. The rope is 2 yards long and a plane view (from above) of the shed and field is shown below. Use this information for Parts A and B below.

Part A: Calculate the area of grass that the goat can eat.
Part B: What length of rope would enable the goat to eat 30 square yards of grass? Show all your reasoning.

Answer 1

• 9.42 yd²
• 3.57 yd

Explanation:

Part A

The area of circle with radius of 2 yd (the length of the rope) is:

• A = π*r² = 3.14*2² = 12.56 yd²

Since 1/4 of the circle is occupied by the shed, the area of the grass is:

• 12.56*3/4 = 9.42 yd²

Part B

Let the area be 30 yd², finding the r as per above formula:

• 3/4*3.14*r² = 30
• r² = 30*4/3*3.14
• r² = 12.74
• r = √12.74
• r = 3.57 yd