If a new sprinkler system has a radius that is 20 meters farther than the old system, what is the circumference of the spraying area?

To determine the circumference of the spraying area for the new sprinkler system, one must apply the formula for the circumference of a circle, which is given by ( C = 2\pi r ), where ( r ) is the radius.

In this case, the new sprinkler system has a radius that is 20 meters greater than the radius of the old system. If we denote the radius of the old system as ( r ), then the radius of the new system would be ( r + 20 ).

Substituting this new radius into the circumference formula gives us:

[

C = 2\pi(r + 20)

]

If we choose a specific example for ( r ) in order to calculate ( C ), let's assume the radius of the old system was 50 meters, making the radius of the new system 70 meters (50 + 20). Therefore, the circumference would be:

[

C = 2\pi(70) \approx 2 \times 3.14 \times 70 = 439.6 \text{ meters}

]

This matches the correct answer, as it accurately reflects the formula for circumference and the addition of the additional 20 meters to the radius