a carabao is tied to one corner of a square plot of side 16m by a rope 7m long. find the area it can graze



The carabao is tied to one corner of a square plot with a rope of length 7 meters. The area that the carabao can graze is limited by the length of the rope and the fact that it is tied to the corner. Since the carabao is tied at the corner of the square plot, it can graze over a quarter circle, with a radius equal to the length of the rope.

The formula for the area of a circle is:

\[
A = \pi r^2
\]

Since the carabao can only graze in a quarter of a circle, the area it can graze will be:

\[
A = \frac{1}{4} \pi r^2
\]

Given the length of the rope (radius \(r = 7\) meters), we substitute this into the formula:

\[
A = \frac{1}{4} \pi (7^2)
\]
\[
A = \frac{1}{4} \pi (49)
\]
\[
A = \frac{49\pi}{4}
\]

Now, using \( \pi \approx 3.1416 \):

\[
A \approx \frac{49 \times 3.1416}{4} = \frac{153.9384}{4} = 38.4846 \, \text{m}^2
\]

Thus, the carabao can graze approximately **38.48 square meters** of land.

Would you like more details or have any questions?

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Here are five related questions to expand on the topic:

1. What would the grazing area be if the rope was 10 meters long instead of 7 meters?
2. How much more area would the carabao be able to graze if it were tied to the center of one side of the square?
3. What if the carabao could graze the entire circle (360 degrees) instead of a quarter-circle?
4. If the square plot had a side of 20 meters instead of 16 meters, how would that affect the grazing area?
5. How would the grazing area change if the rope was doubled in length?

**Tip:** When calculating areas involving circles, always remember that fractions of circles (like half, quarter, or any portion) simply scale the total area formula by the corresponding fraction.

A carabao is tied to one corner of a square plot of side 16m by a rope 7m long. Find the area it can graze.

Learn how to calculate the grazing area for a carabao tied to the corner of a square plot with a 7-meter rope. Using the formula for the area of a quarter-circle, this problem explains key geometry concepts, including circle area calculations. Suitable for students in Grades 6-8.

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