Question

salam orders a center pivot irrigation system to water his fields. the system is made up of a line of connected pipes that turn around a center point. salams system will be 1,150 ft long.
a. what is the longest distance across the space the system will water? show your work.
b. check your answer to problem 3a. show your work.

Explanation:

Step1: Recall the relationship between radius and diameter

The irrigation system forms a circle. The length of the pipes is the radius \( r = 1150\) ft. The formula for the diameter \( d\) of a circle is \( d = 2r\).

Step2: Calculate the diameter

Substitute \( r = 1150\) into the formula \( d = 2r\). So \( d=2\times1150 = 2300\) ft.

Step1: Use the radius - diameter relationship in reverse

If the diameter \( d = 2300\) ft, then the radius \( r=\frac{d}{2}\).

Step2: Calculate the radius from the diameter

Substitute \( d = 2300\) into \( r=\frac{d}{2}\). So \( r=\frac{2300}{2}=1150\) ft, which matches the given length of the pipes (radius of the circular irrigation area).

Answer:

The longest distance across the space (the diameter of the circular area) is \( 2300\) ft.

For part b (checking the answer):