Get In Line






Exploring Circumference and Perimeter

Materials: Scientific Calculator

In-line skating has become a popular city sport. The parks department is thinking of constructing ramps in some of the local playgrounds. A "half-pipe" ramp is formed by two quarter circle ramps each 10 feet high with a flat space of 20 feet between the diameters.



1. Find the distance a skater travels from the top of one ramp to the top of the other. (hint: What is the length of AB?)


2. Another launch ramp is formed by 2 arcs each with a central angle of 60 degrees and a radius of 10 ft. Find the length from the top of one ramp to the top of the other. (Hint: What fractional part of the circle is each arc?)


3. A third ramp is a straight ramp 4 ft high and 10 ft long with a flat space of 20 ft in point P to point R. (Hint: Use the Pythagorean Theorem)



Thinking Cap

A school track is formed by 2 straight segments joined by 2 half circles. Each segment is L long and each half circle diameter is D in length. Write a formula for finding the distance, D, around the track.



For The Teacher: Get in Line


Using the Activity:

In this activity, students can use the calculator to find the lengths of three different ramps in-line skaters might use. Students will use the pi, square, and square-root keys on the calculator. The teacher may want to review the formula for finding the circumference (perimeter) of a circle. Discuss how to find the lengths of various arcs of the circle. To find the length of the third ramp, students will need to use the Pythagorean Theorem.

Another important extension to this activity is finding the steepness of the various ramps. Students can use this data to determine the level of difficulty of each ramp.

Answers:

First ramp: 51.41592654 ft.

The length of the arc AB is one quarter the circumference of the circle.

Second ramp: 40.943951 ft

The length of the arc is one sixth the circumference of the circle.

Third ramp: 41.540659 ft

The length of the ramp x is found by using the pythagorean theorem.


Discussion Questions:

1. What makes one ramp better than another?

2. Which ramp is safest? Why?

3. Which is the construction is more challenging? Why?


Thinking Cap:

D = 2L + (2)(1/2)(Pi)d = 2L + (Pi)d


Submitted by: Ann Mele, Assistant Principal, Offsite Educational Services; NY Public Schools; NY, NY