Tennis balls are sold in cylindrical containers that contain three balls each. The tennis balls and container can be modeled as follows.
The container, lying on its side, passes through an X-ray scanner in Tallahassee International Airport, where Jordan works as a security guard. Depending on the opacity of the container and the balls, what should Jordan expect to see when she reads the screen of the X-ray scanner? Explore the applet by adjusting the opacity of the container and the tennis balls.
Izabella and her friends are ordering pizza from their favorite spot. They can afford to buy either two inch pizzas or one inch pizza. The thickness of the pizza is the same for each.
It is given that the pizzas have the same thickness. Therefore, areas of the pizzas will determine the best option. Begin by modeling the pizzas as circles with diameters of and inches.
Recall that Izabella and her friends can afford two inch pizzas. As a result, the best option is to buy a inch pizza. One of the friends was so close to ordering the two 9-inch pizzas. Thanks for helping them make the right choice.
The Knights of the Round Table are the highly-esteemed knights of the mythical fellowship of King Arthur. In the beginning, there were only twelve knights. They met at the Round Table that is a symbol of equality among all of its legendary members.
Assume that each knight has the same circular chair around the Round Table whose radius is feet. Given that all chairs and the Round Table are externally tangent to each other, what is the radius of each chair? Round the answer to the nearest tenth.
The Round Table and the chairs can be modeled by using circles.
By labeling the centers of the inner circle and two adjacent outer circles, a triangle passing through these centers can be drawn.
Notice that is an isosceles triangle where From here, to find the value of the vertex angle of needs to be found. Since there are chairs, the measure of can be found by dividing by Now that the measure of the vertex angle was found, the altitude of the base can be drawn to use the trigonometric ratios. Remember that the altitude of the base of an isosceles triangle bisects the vertex angle and the base.
Jordan and Ali are comparing their weights. Jordan is feet tall, and Ali is feet tall. Their shoulder widths are foot and feet, respectively.
When a body is modeled using a cylinder, one's height and shoulder width will represent the cylinder's height and diameter, respectively.
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
Arc measure is also an important concept to interpret the situations modeled by circles. For example, consider a time zone wheel.
A time zone wheel is a tool used to find the time in different locations across the world. For example, to find the time in Tokyo when it is in Amsterdam, rotate the small wheel until the labels of and Amsterdam align.
As can be seen, it is in Tokyo.
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.