10.6.4 Calculator Exploration: Areas of Circles
The calculator can be accessed on the left-hand side bar under Toolkit.
Finding the Area of a Circle
The formula for the area of a circle is:
The Globe Theater in London, England, is approximately circular in shape and has a diameter of about 100 feet. Suppose that you want to find the area it occupies. The formula for the area of a circle includes the radius, so the first step is to find the radius of the circle. This is half the diameter. So the radius of the theater is 100 feet divided by two, which equals 50 feet.
Now the value for the radius can be substituted into the formula.
The area occupied by the theater = = 7853.98 square feet to 2 decimal places.
However, since the diameter was not measured accurately, a more reasonable estimate for the area is about 8,000 square feet.
Activity: Building Designs
Calculate the areas of the following road and town developments, assuming that the measurements are sufficiently accurate to allow answers to the nearest whole number.
(a) A traffic circle of radius 15.6 yards.
Units for area are square units, for example, square feet or square yards.
(a) The area of a circle = .
So the area of the traffic circle = square yards, to the nearest whole number.
(b) A circular building of diameter 54 meters.
Remember that you need the radius, not the diameter for the formula for area of a circle.
(b) Here you are given the diameter. The radius is half the diameter.
So radius =
So, the area of the circular building = , to the nearest whole number.
(c) A semicircular lecture hall of diameter 150 feet.
(c) The area of a semicircle is half the area of a circle. So the area of a semicircle = .
The lecture hall has a diameter of 150 feet, so the radius is 75 feet.
The area of the lecture hall = , to the nearest whole number.
The following formulas can be used to calculate the area of various shapes:
- Add these to your math notebook now if you haven't already done so.