A horse is tethered to the corner of a rectangular field 50 m by 20 m by a 14 m long rope. The area of the field that it can graze is?
Understand the Problem
The question describes a scenario where a horse is tethered to the corner of a rectangular field with a rope. We need to calculate the area the horse can graze, this area will be a section of a circle.
Answer
$154 \ m^2$
Answer for screen readers
(b) $154 \ m^2$
Steps to Solve
- Visualize the Problem
Imagine a horse tethered to the corner of a rectangular field. The horse can graze in a quarter-circle because it's restricted by the sides of the rectangle.
- Find the Area of the Full Circle
The rope's length is the radius of the circle. The area of a full circle is given by the formula: $A = \pi r^2$ where $r$ is the radius. In our case, $r = 14$ m. Using $\pi = \frac{22}{7}$, the area of the full circle would be: $A = \frac{22}{7} \times 14 \times 14$
- Calculate the Area of the Quarter Circle
Since the horse can only graze a quarter of the circle due to the rectangular field's corner, we divide the full circle's area by 4. Area of quarter circle $= \frac{1}{4} \times \frac{22}{7} \times 14 \times 14$
- Simplify the Expression
Simplify the expression to find the area the horse can graze: Area $= \frac{1}{4} \times \frac{22}{7} \times 14 \times 14 = \frac{1}{4} \times 22 \times 2 \times 14 = \frac{1}{4} \times 616 = 154$
(b) $154 \ m^2$
More Information
The area the horse can graze is a quarter of a circle because it is tethered to the corner of a rectangular field. The radius of this circle is the length of the rope. The area is therefore $154 \ m^2$.
Tips
A common mistake is calculating the area of the full circle instead of the quarter circle. Remember the horse is tethered to the corner of the field.
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