students measured the diameters and circumferences of the tops of a variety of cylinders. Below are the data that they collected. estimate the diameter of a cylinder with circumference 22cm.
Cylinder Tops
Diameter(cm) 3,3,5,6,8,8,9.5, 10, 10, 12
Circumference(cm) 9.3,9.5, 16, 18.8, 25, 25.6,31.5, 30.9, 39.5
To estimate the diameter of a cylinder with a circumference of 22 cm, we can make use of the collected data and find a relationship between the diameters and circumferences of the cylinders.
First, let's organize the data:
Diameter (cm): 3, 3, 5, 6, 8, 8, 9.5, 10, 10, 12
Circumference (cm): 9.3, 9.5, 16, 18.8, 25, 25.6, 31.5, 30.9, 39.5
To find the relationship between diameter and circumference, we can calculate the ratio of the circumference to the diameter for each cylinder:
Ratios: 9.3/3, 9.5/3, 16/5, 18.8/6, 25/8, 25.6/8, 31.5/9.5, 30.9/10, 39.5/10
In order to estimate the diameter for a given circumference of 22 cm, we need to find the ratio that is closest to 22/7 (the approximation for the mathematical constant pi).
Let's calculate the ratios:
Ratios: 3.1, 3.2, 3.2, 3.1, 3.1, 3.2, 3.3, 3.1, 3.9
Comparing these ratios to 22/7, the closest ratio is 3.1.
Therefore, based on the collected data, the estimated diameter of a cylinder with a circumference of 22 cm would be approximately 3.1 cm.