Question

: A cow is tethered by a rope 50 m long. The rope is fastened to a hook which is located 10 m from the center on the longer side of barn. The barn measures 60 m by 30 m. Over how much ground can the cow graze?Direction:1. What are problem solving strategies to be used to solve the Problem 2? Describe in your own words.

Answer 1

First, we have to consider the area covered by the cow when the rope is fully extended. This is a semicircle of radius 50 in front of the barn,

Let's say the cow goes to the left. When it reaches the end of the barn, the rope will have 10 more meters to turn,

Similarly, if the cow goes to the right of the barn, there will be 20 meters of the rope on the side of the barn and the cow will have another 30 meters to turn,

In summary, the area that can be covered by the cow will be the sum of the area of the semicircle with radius 50 m (area A), the area of the quarter of a circle of radius 10 m (area B) and the area of the quarter of a circle with radius 30 m (area C),