A cow is tied with a rope of length 14 m at the corner of rectangular field measured 20 m by 16 m. Find the area of the field in which the cow can graze.
#anyone to help me with proper and systematic step by step solution
draw a diagram of the corner of the field. Since the rope is shorter than either dimension, the grazed area is just a 1/4 circle.
You know how to figure the area of a circle, right?
To find the area of the field in which the cow can graze, we need to determine the area of the circle that the cow can reach when it is tied with a rope.
Step 1: Visualize the problem
Draw a diagram of the rectangular field and mark the location of the cow, which is tied at one of the corners. You can draw a circle around the cow to represent the area it can reach while tied with a rope.
Step 2: Identify the relevant measurements
From the problem, we are given that the rope has a length of 14 meters, and the rectangular field has dimensions of 20 meters by 16 meters.
Step 3: Determine the radius
The rope tied to the cow represents the radius of the circle. So, the radius of the circle is 14 meters.
Step 4: Find the area of the circle
The formula to find the area of a circle is A = πr^2, where A is the area and r is the radius. We have the radius as 14 meters, so we can substitute it into the formula:
A = π(14^2)
A = π(196)
A = 615.75 square meters (approximated)
Therefore, the area of the field in which the cow can graze is approximately 615.75 square meters.