Honors Geometry Companion Book, Volume 1

1.2.1 Using Formulas in Geometry (continued) Example 3 Finding the Circumference and Area of a Circle

The circumference of a circle is the distance around a circle. The circumference of a circle is similar to the perimeter of a figure since both are the measure of the total distance around the figure. A circle’s circumference depends on the length of its radius (a segment whose endpoints are the center and a point on the circle) or on the length of its diameter (a segment that passes through the center of the circle and whose endpoints are on the circle). The length of a circle’s diameter is always twice the length of its radius, d = 2 r . The formula for the circumference of a circle is C = 2 πr , where r is the radius of the circle.

Alternatively, since the diameter d of a circle is equal to twice the radius ( d = 2 r ), the circumference of a circle can also be found using the formula C = πd . The formula for the area of a circle is A = πr 2 . Pi ( π ) is the ratio of a circle’s circumference to its diameter. The value of π is approximated as 3.14, unless otherwise stated. In this example, the circumference and area are found for a circle with radius 5 inches. To find the circumference and the area, simply substitute 5 into each formula for r and simplify. When the circumference is found, the first step after substituting 5 is to multiply 2 and 5, and the result is 10 π . This answer is in terms of π . To find an approximate decimal value of the circle’s circumference, substitute the approximate value of π , 3.14, into the expression 10 π and multiply. If the directions had said to find the circle’s area in terms of π , the answer would have been A = 25 π . As with the calculation of circumference, to find the approximate decimal value of the circle’s area, substitute 3.14 into the expression 25 π and multiply.


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