diameter. Since the diameter is twice the radius, circumference can - PowerPoint PPT Presentation

D AY 142 – A PPLICATIONS OF CIRCUMFERENCE

I NTRODUCTION We encounter circular objects in real life such as cakes, rings, tires, and pizzas. The distance between them depends on their diameter. Other objects such as satellites and planes follow circular paths. The distance that they move can be calculated as a circumference or as a fraction of a circumference. In this lesson, we will discuss applications of a circumference.

V OCABULARY Orbit This is path followed by an object that is moving around another object in space.

The circumference of a circle is calculated by the formula 𝐷 = 𝜌𝐸 where C is the circumference, D the diameter and 𝜌 is the ratio of the circumference to the diameter. Since the diameter is twice the radius, circumference can be calculated by the formula 𝐷 = 2𝜌𝑠, where r is the radius of the circle. Circumference has many applications in real life. We will discuss some of this applications.

The path of a satellite 1. A satellite follows a circular path around the earth. If the radius of the earth is r and the distance from the earth to the satellite is 𝑒, then the total radius of the satellite’s orbit is 𝑠 + 𝑒 . 𝑒 𝑠 + 𝑒 𝑠 Circumference of the path = 2𝜌 𝑠 + 𝑒 .

2.Circular buildings The circumference of a circular building is determined by the radius of that building. Initially, a string of a certain radius is tied at a point and then a circle is drawn around that point. The wall of the building is constructed along that circle. 3. Merry-go-round The distance moved by a child on the merry-go- round in one revolution is equivalent to the circumference of the merry-go-round.

Example 1 A child makes 5 revolutions on a merry-go-round. If the distance from the center of the merry-go-round is 5 𝑔𝑢, find the total distance covered by the child around the merry-go-round. Solution Radius of the merry-go-round = 5 𝑔𝑢 Distance in one revolution = C = 2 × 3.142 × 5 = 31.42 𝑔𝑢 Distance in 5 revolutions = 31.42 × 5 = 157.1 𝑔𝑢

4.Rings Rings are always circular in shape. At times a person may want to be made a ring that exactly fits his/her finger. If a string is tired around the finger, the length of the string will reveal the circumference of the finger. From this circumference the diameter of the ring can be calculated. 5. Baking Some pizzas and cakes are circular. Their size is determined by the diameter of pan used to bake them.

HOMEWORK A car moves for a distance of 942.6 𝑔𝑢. If the tire of the car made 100 revolutions, calculate the radius of the tire.

A NSWERS TO HOMEWORK 1.5 𝑔𝑢

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