Math I
Unit 6 – Notes Circles
Name: ______________________________
A circle is defined as all points in a plane that are an equal distance from a point called the center. The
circle is named by the center point.
Circumference, C, is the distance around the outside of a circle. C  2r or C  d
Find the circumference of each of the following circles. Give your answer in 2 forms: the first in
terms of π, and then rounded to the nearest hundredth. Use the π button on your calculator.
1.
2.
3.
4.
C = ______
C = ______
C = ______
C = ______
C ≈ ______
C ≈ ______
C ≈ ______
C ≈ ______
5.
6.
7.
8.
C = ______
C = ______
C = ______
C = ______
C ≈ ______
C ≈ ______
C ≈ ______
C ≈ ______
The formula for the area of a circle is A  r 2 . To prove why this formula works, we need to split the
circle into sections and place them side by side. The sum of the two lengths of the new shape is equal to
the circumference, C, of the circle 2r . The shape has a width r which is equal to the radius of the circle.
When the sections are place side by side, they form a shape that is similar to a parallelogram. If these
sections were cut smaller and smaller, the shape they would form when placed side by side would look
more and more like a perfect rectangle.
The width of this shape is r, the radius of the circle and the length r . The area of the new shape is equal
to that of the original circle and since area of a rectangle is l  w , therefore, area of the shape and the
circle is r r  r 2 .
Find the area of the following circles. Give your answer in 2 forms: the first in terms of π, and then
rounded to the nearest hundredth. Use the π button on your calculator.
9.
10.
11.
12.
A = ______
A = ______
A = ______
A = ______
A ≈ ______
A ≈ ______
A ≈ ______
A ≈ ______