Question

lesson 6 | session 1

1. 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: Identify radius - length relationship

The center - pivot irrigation system forms a circle, and the length of the system is the radius $r$ of the circle. Given $r = 1150$ ft. The longest distance across a circle is the diameter $d$. The formula for the diameter of a circle is $d = 2r$.

Step2: Calculate the diameter

Substitute $r=1150$ ft into the formula $d = 2r$. So, $d=2\times1150 = 2300$ ft.

Step3: Check the answer

We know that if we divide the diameter $d$ by 2, we should get the radius $r$. $\frac{d}{2}=\frac{2300}{2}=1150$ ft, which is the original radius value. So our answer is correct.

Answer:

a. The longest distance across the space the system will water (the diameter) is 2300 ft.
b. The check is shown in Step 3 above.