# Graphing a Linear Relationship

Objective:To verify the linear relationship between the circumference and the diameter of circular objects by taking experimental data and utilizing graphical techniques.

Introduction :The distance around a circle is called its circumference. A simple experiment can be conducted to aid in understanding the formula for the circumference of the circle. Use a piece of string to measure the distance around a circular object. Measure the diameter and then divide the circumference by the diameter. The result of this measurement is an approximation for the number π,(pi). (John Murray, 1989 )

π = Circumference = C

Diameter D

An alternate version of this formula is

C = π D

Pi is not a rational number but for this experiment ,a figure of 3.14 as an approximation of pi will be used when required.

The value of the circumference and diameter for each respective circular object can form a best fit line graph by let the x-axis being the diameter (cm) and the y-axis being the circumference (cm).If the slope of a line and a particular point on the line are known, it is possible to find the equation of the line. Suppose the slope of a line is m and (x1 , y1) is a particular point on the line. Let (x, y) be any other point on the line. Then, by the definition of the slope,

m = y1 - y2

x1 - x2

Materials:100ml beaker, 50ml measuring cylinder, 250ml beaker, meter ruler, filter funnel, marker pen, ball pen, strand of retort stand, 1500ml tupperware, stand of chair, Dettol cover ,trolley handle, door handle, water pipe, electric blower hose, fire extinguisher tube, vernier calipers, string and linear graph paper.

Method

1) Vernier caliper is used to measure the diameter and the circumference of 8 or more circular objects provided. 2) The circumference of circular objects will be determined by a piece of string. 3) Other larger or smaller objects located in the lab may be included in the measurements. 4) The measured values in units of centimeters are recorded.

Result

|Object |Circumference (cm) |Diameter (cm) | | |1st |2nd |3rd | |100ml Beaker |17.00 |5.19 |3.28 | |50ml Measuring cylinder |8.70 |2.50 |3.48 | |250ml Beaker |22.8 |7.07 |3.22 | |Filter funnel |2.77 |0.83 |3.34 | |Marker pen |5.00 |1.50 |3.33 | |Ball pen |3.13 |0.96 |3.26 | |Stand of retort stand |3.57 |1.08 |3.31 | |1500ml Tupperware |28.70 |8.90 |3.22 | |Stand of chair |7.73 |2.30 |3.26 | |Dettol cover |11.50 |3.36 |3.36 | |Handle of trolley |8.70 |2.57 |3.39 | |Handle of door |10.67...

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