A sprinkler set to angle 220. It can water area aprox. 20 square meters. Find the distance that the springier can spray water

To find the distance that the sprinkler can spray water, we can model the watered area as a sector of a circle. The formula for the area of a sector is:

\[
A = \frac{\theta}{360} \times \pi r^2
\]

Where:
- \(A\) is the area of the sector (20 square meters),
- \(\theta\) is the central angle of the sector (220 degrees),
- \(r\) is the radius or distance that the sprinkler sprays (which we want to find).

### Step-by-step Solution:

1. Use the formula for the area of a sector:

\[
20 = \frac{220}{360} \times \pi r^2
\]

2. Simplify the angle fraction:

\[
\frac{220}{360} = \frac{11}{18}
\]

3. Now substitute this into the equation:

\[
20 = \frac{11}{18} \times \pi r^2
\]

4. Solve for \(r^2\) by isolating it:

\[
r^2 = \frac{20 \times 18}{11 \times \pi}
\]

5. Compute the values:

\[
r^2 = \frac{360}{11 \pi}
\]

6. Simplifying:

\[
r^2 \approx \frac{360}{34.5575} \approx 10.418
\]

7. Finally, find \(r\) by taking the square root:

\[
r \approx \sqrt{10.418} \approx 3.23 \text{ meters}
\]

### Conclusion:
The sprinkler can spray water approximately **3.23 meters**.

Would you like more details on any step?

Here are 5 related questions:
1. How would the result change if the angle was different?
2. What if the area covered by the sprinkler was 30 square meters?
3. Can you explain how the area of a circle relates to sectors?
4. How would the formula change if the sprinkler covered a full circle (360 degrees)?
5. How can this method be applied to irregularly shaped gardens?

**Tip:** Understanding how sectors of a circle work can help solve many real-life problems involving angles and areas!

A sprinkler set to angle 220. It can water area approx. 20 square meters. Find the distance that the sprinkler can spray water.

Learn how to calculate the distance a sprinkler can spray when set to an angle of 220 degrees and covering an area of 20 square meters. This problem involves understanding the formula for the area of a sector and applying basic circle geometry. Ideal for students in Grades 9-11.

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