A circle is the set of all points in a plane at a given distance (called the radius ) from a given point (called the center.)
A line segment connecting two points on the circle and going through the center is called a diameter of the circle.
Clearly, if represents the length of a diameter and represents the length of a radius, then .
The circumference of a circle is the distance around the outside. For any circle, this length is related to the radius by the equation
The area of a circle is given the formula
What is the area of a circular table with diameter ft?
Given that, the diameter of the circular table is ft.
So, the radius of the circular table is half of the diameter. That is, radius is ft.
Use the formula for area of a circle, , where is the radius of the circle.
Substitute for in the formula.
Therefore, the area of the circular table is about
What is the area of the shaded region in the figure shown?
It's clearly marked that the larger circle has a radius cm. So, its area is
What about the smaller circle? Well, the distance from the center to edge is cm; the diameter of the smaller circle is cm. So, the radius of the smaller circle is cm.
To get the area of the shaded region, subtract the area of the smaller circle from the area of the larger circle.
Therefore, the area of the shaded region is about .