What if you wanted to figure out the area of a circle with a radius of 5 inches?
Area of a Circle
First, take a circle and divide it up into several wedges, or sectors. Then, unfold the wedges so they are all on one line, with the points at the top.
Finding the Area
Find the area of a circle with a diameter of 12 cm.
Finding the Radius
Work backwards on this problem. Plug in the area and solve for the radius.
Calculating the Area of a Circle Inscribed in a Square
A circle is inscribed in a square. Each side of the square is 10 cm long. What is the area of the circle?
The diameter of the circle is the same as the length of a side of the square. Therefore, the radius is half the length of the side, or 5 cm.
Earlier Problem Revisited
Find the area of the shaded region from Example C.
The area of the shaded region would be the area of the square minus the area of the circle.
First, use the formula for the area of a circle to solve for the radius of the circle.
If the radius is 6 units, then the diameter is 12 units.
Find the area of a circle with diameter 20 inches.
Find the area of the shaded region. Round your answer to the nearest hundredth.
- Carlos has 400 ft of fencing to completely enclose an area on his farm for an animal pen. He could make the area a square or a circle. If he uses the entire 400 ft of fencing, how much area is contained in the square and the circle? Which shape will yield the greatest area?
To view the Review answers, open this PDF file and look for section 10.10.