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 horse tied to the corner of a rectangular field and asks for the area the horse can graze, given the dimensions of the field and the length of the rope. The problem can be solved by finding the area of a circle sector.
Answer
(b) $154 m^2$
Answer for screen readers
(b) $154 m^2$
Steps to Solve
- Identify the shape of the grazing area
Since the horse is tied to a corner, it can graze in a quarter-circle shape. 2. Recall the area of a circle
The area of a full circle is given by the formula $A = \pi r^2$, where $r$ is the radius. 3. Calculate the area of the quarter-circle
Since the horse can graze a quarter of a circle, we need to divide the area of the full circle by 4. The radius $r$ is the length of the rope, which is 14 m.
Area of the quarter-circle is: $A_{quarter} = \frac{1}{4} \pi r^2$ $A_{quarter} = \frac{1}{4} \pi (14)^2$ $A_{quarter} = \frac{1}{4} \pi (196)$ $A_{quarter} = 49\pi$
Using the approximation $\pi \approx \frac{22}{7}$:
$A_{quarter} = 49 \times \frac{22}{7} = 7 \times 22 = 154$
Therefore, the area the horse can graze is $154 m^2$.
(b) $154 m^2$
More Information
The area that the horse can graze is a quarter of a circle because it is tethered to the corner of a rectangular field.
Tips
A common mistake would be to calculate the area of the full circle instead of the quarter circle. Also forgetting to use $\pi$ in the area calculation.
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