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Explore how much land a cow can graze on when it’s tied to one corner of a 30m by 30m square area with a 21m rope.
A cow is tied to a corner of a square plot of side 30m by a rope 21m long. How much area it can graze?
The cow can graze 1385.44 square metres approximately.
Here’s how
To find the area the cow can graze, we need to find the area of the circular region that the rope creates around the tied corner.
Given that the rope is 21 meters long, this forms a circle with a radius of 21 meters.
The formula for the area of a circle is:
Area = π × radius^2
Where:
- Area is the area of the circle,
- π is a constant approximately equal to 3.14159,
- radius is the radius of the circle.
Plugging in the values:
Area = π × (21)^2
Area = 3.14159 × 441
Area is approximately 1385.44 square meters.
So, the cow can graze approximately 1385.44 square meters of area.
Area and Perimeter of a Circle
The area and perimeter of a circle can be calculated using the following formulas, where:
- r is the radius of the circle (distance from the center to any point on the edge).
- d is the diameter of the circle (distance across the circle passing through the center).
- π (pi) is a mathematical constant approximately equal to 3.14159.
Area:
Perimeter (Circumference):
You can also find the diameter if you know the radius using the formula d = 2r.You can find the radius if you know the diameter using the formula r = d / 2.If you only know the circumference, you can find the radius using the formula r = C / (2π).
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Source: Math Hello Kitty
Categories: Math
