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Based on the features and theorems of the circles, this lesson will relate the circles with the real-life examples.

Catch-Up and Review

Here are some recommended readings before getting started with this lesson.

Example

Modeling Bodies Using Cylinders

Jordan and Ali are comparing their weights. Jordan is feet tall, and Ali is feet tall. Their shoulder widths are foot and feet, respectively.

Modeling Human Bodies With Cylinders

Consider their bodies to be roughly cylindrical, and their shoulder widths could represent the diameter. What is the ratio of Jordan's weight to Ali's weight?

Answer

or

Hint

Volume of a cylinder is the product of the base area and height of the cylinder.

Solution

When a body is modeled using a cylinder, one's height and shoulder width will represent the cylinder's height and diameter, respectively.

Cylinders

By comparing the volumes of these cylinders, a relation between the weights of Jordan and Ali can be set up. To do this, the radii of the cylinders should be found. Recall that the radius of a cylinder is half of its diameter.

Now that the radii have been found, the formula for the volume of a cylinder can be used to find their volumes.

The volumes of the cylinders imply that if Jordan weighs pounds, Ali weighs pounds. Therefore, the ratio of Jordan's weight to Ali's weight is or

Closure

Modeling Real Life Situations Using Circles

In real life, there are plenty of situations where circles can be appreciated. In this lesson, a few common situations have been covered. How about some other fun ones? Take, for example, one of the most complex applications of circles — the global positioning system.

GPS
When the three circular regions scanned by each satellite intersect, the position of the device is determined. Much more detail can be learned about GPS, this is just a brief introduction. How else are circles used in everyday life?
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