# Get In Line

Exploring Circumference and Perimeter

Materials: Scientific Calculator

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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