To determine the area watered by the sprinkler, we need to find the area of a sector of a circle, since the sprinkler waters a section of the circular area.

Step-by-Step Solution

1. Identify Given Values:

   • Radius of the circle $r = 43$ feet (the distance the sprinkler sprays).
   • Angle swept by the sprinkler $\theta = 4.9$ radians.

2. Formula for the Area of a Sector: The area $A$ of a sector with radius $r$ and angle $\theta$ (in radians) is given by: $A = \frac{1}{2} r^2 \theta$

3. Substitute Values: $A = \frac{1}{2} \times 43^2 \times 4.9$ Calculating this step-by-step:

   • $43^2 = 1849$
   • $1849 \times 4.9 = 9060.1$
   • $\frac{1}{2} \times 9060.1 = 4530.05$

4. Final Answer: The area of the lawn that the sprinkler has watered is approximately: $4530.05 \text{ square feet}$

Would you like further details on this calculation or have any questions?

Related Questions

1. How would the area change if the sprinkler covered an angle of 3 radians?
2. What would be the area if the sprinkler distance increased to 50 feet?
3. How is the sector area formula derived?
4. If the sprinkler rotated a full circle, what area would be covered?
5. What happens to the area if the angle decreases by half?

Tip

Always use radians when calculating sector areas in a circle, as the formula $A = \frac{1}{2} r^2 \theta$ assumes the angle is in radians.