10.6.4 Calculator Exploration: Areas of Circles

Calculator IconThe 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:

area equals pi multiplication open radius close squared

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 = pi multiplication open 50 feet close squared = 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 Symbol 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.

Hint Symbol

Comment

Units for area are square units, for example, square feet or square yards.

Solution Symbol

Answer

(a) The area of a circle = pi multiplication open radius close squared.

So the area of the traffic circle = pi multiplication open 15 .6 yds close squared almost equals 765 square yards, to the nearest whole number.

(b) A circular building of diameter 54 meters.

Hint symbol

Comment

Remember that you need the radius, not the diameter for the formula for area of a circle.

Solution Symbol

Answer

(b) Here you are given the diameter. The radius is half the diameter.

So radius = 54 m division two equals 27 m

So, the area of the circular building = pi multiplication open 27 m close squared almost equals two comma 290 times m super two, to the nearest whole number.

(c) A semicircular lecture hall of diameter 150 feet.

Solution Symbol

Answer

(c) The area of a semicircle is half the area of a circle. So the area of a semicircle = one divided by two multiplication pi multiplication open radius close squared.

The lecture hall has a diameter of 150 feet, so the radius is 75 feet.

The area of the lecture hall = one divided by two multiplication pi multiplication open 75 ft close squared almost equals eight comma 836 times ft super two, to the nearest whole number.

To recap:

  • The following formulas can be used to calculate the area of various shapes:

    Area of a rectangle equals length multiplication width
    Area of a parallelogram equals base multiplication height
    Area of a triangle equation left hand side equals right hand side one divided by two postfix multiplication base multiplication height
    Area of a circle equation left hand side equals right hand side pi multiplication open radius close squared
  • Add these to your math notebook now if you haven't already done so.

10.6.3 Tangram Areas Again

10.6.5 Making a Garden