How can the information about a…

Mathematics Questions

How can the information about a bicycle wheel with a diameter of 63 centimeters and a distance traveled of 198 centimeters help estimate the value of π?

Short Answer

The diameter of the bicycle wheel is 63 centimeters, and it covers 198 centimeters in one full rotation. By applying the formula for circumference (C = π * d), we find that π can be approximated as 7/22.

Step-by-Step Solution

Step 1: Identify the Wheel’s Dimensions

To begin with, determine the diameter of the bicycle wheel. In this case, it is given as 63 centimeters. This information is crucial as it will be used to calculate the circumference of the wheel.

Step 2: Understand Wheel Circumference

Next, we will look at the circumference of the wheel, which represents the distance the bicycle travels in one full rotation. According to the information provided, the wheel covers 198 centimeters when it completes one full rotation.

Step 3: Relate Diameter to Circumference using π

Finally, we will use the formula for circumference, which is π multiplied by the diameter (C = π * d). Plugging in the values, we get π * 63 = 198. To solve for π, rearrange the equation resulting in π = 198 / 63, leading to π being approximately 7/22.

Related Concepts

Diameter

The straight line distance passing from side to side through the center of a circle or wheel

Circumference

The distance around the edge of a circle or wheel, calculated as the diameter multiplied by ϊ

Ί

A mathematical constant approximately equal to 3.14159 used to relate the diameter of a circle to its circumference.

Scroll to Top