Question

annas younger brother and sister went on a carnival ride that has two separate circular tracks. annas brother rode in a blue car that travels a total distance of 220 feet around the track. annas sister rode in a green car that travels a total distance of 126 feet around the track. anna drew a sketch of the ride. what is the difference between the radii of the two circular tracks? 3 of 4 questions the distances of 220 feet and 126 feet represent the select... of each circular track. use 3.14 for \\( \pi \\) the radius of the circle made by annas brother in the blue car is about select... feet. use 3.14 for \\( \pi \\) the radius of the circle made by annas sister in the green car is about select... feet. the difference between the radii of the two circles is about select... feet.

Explanation:

Step1: Recall the circumference formula

The formula for the circumference of a circle is \(C = 2\pi r\), where \(C\) is the circumference and \(r\) is the radius. The distances 220 feet and 126 feet represent the circumferences of each circular track.

Step2: Find the radius of the blue - car track

Given \(C_{blue}=220\) feet and \(\pi = 3.14\). From \(C = 2\pi r\), we can solve for \(r\): \(r=\frac{C}{2\pi}\).
Substitute \(C = 220\) and \(\pi=3.14\) into the formula: \(r_{blue}=\frac{220}{2\times3.14}=\frac{220}{6.28}\approx35\) feet.

Step3: Find the radius of the green - car track

Given \(C_{green}=126\) feet and \(\pi = 3.14\). Using \(r=\frac{C}{2\pi}\), substitute \(C = 126\) and \(\pi = 3.14\): \(r_{green}=\frac{126}{2\times3.14}=\frac{126}{6.28}\approx20\) feet.

Step4: Calculate the difference in radii

The difference \(\Delta r=r_{blue}-r_{green}\). Substitute \(r_{blue}\approx35\) and \(r_{green}\approx20\): \(\Delta r = 35 - 20=15\) feet.

Answer:

The distances of 220 feet and 126 feet represent the circumference of each circular track.
The radius of the circle made by Anna's brother in the blue car is about 35 feet.
The radius of the circle made by Anna's sister in the green car is about 20 feet.
The difference between the radii of the two circles is about 15 feet.