Circles. A circle is a shape with all points the same distance from its center. The distance around...
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Transcript of Circles. A circle is a shape with all points the same distance from its center. The distance around...
Circles
A circle is a shape with all points the same distance from its center.
The distance around a circle is called its circumference.
The distance across a circle through its center is called its diameter.
(pi) is the ratio of thecircumference of a circle to its
diameter. For any circle,if you divide its circumference by its
diameter, you get avalue close to 3.14159. This
relationship is expressed in thefollowing formula: C/D = where C is the circumference and D is the
diameter.
The radius of a circle is the distance from the center of a circle to a point on the circle. If you place two radii end-to-end in a circle, you would
have the same length as one diameter. So a circle's diameter is
twice as long as its radius.
The formula for the circumference of a circle is given by either :
πr C dC 2or
Example : The diameter of a circle is 3 cm. What is its
circumference? (Use = 3.14)
Solution: C = dC = 3.14 · (3 cm)C = 9.42 cm
3 cm
Example : The radius of a circle is 2 in. What is its
circumference? (Use = 3.14)
inC
C
rC
56.12
214.32
2
Example : The circumference of a circle is 15.7 cm. What isits diameter? (Use = 3.14)
• C = d
15.7 cm = 3.14 · d
d = 15.7 cm ÷ 3.14
d = 5 cm
The area of a circle is the number of square units inside that circle. If each square in the
circle below has an area of 1 sq.cm, you could count the total number of squares to get the area of this circle. If there were a
total of 28.26 squares, the area of this circle would be 28.26 csq.m
The area of a circle is given by the formula
2rA
Example : The radius of a circle is 3 in. What is its area?
(Use = 3.14)• Solution: A = · r · r• A = 3.14 · (3 in) · (3 in)• A = 3.14 · (9 sq.in)• A = 28.26 sq.in
Example: The diameter of a circle is 8 cm. What is its area?
(Use = 3.14)
• r = 4 cm• A = · r · r• A = 3.14 · (4 cm) · (4 cm)• A = 50.24 sq.cm
Example: The area of a circle is 78.5 sq.m. What is its radius? (Use = 3.14)
• Solution: A =• 78.5 sq.m = 3.14 ·• 78.5 sq.m ÷ 3.14 =• 25 sq.m =• r = 5 m
2r2r2r
2r
2r
Find the area of the rectangular piece of metal after the 2 circles are
removed.
28.00 cm
45.00 cm
10.00 cm16 cm
Find the perimeter and area of the shape.
inP
P
P
CP
CCP
64.160
64.8179
0.2614.379
5.3922
15.39
2
15.39
2
2
66.1557
66.5301027
0.1314.30.265.39
inA
A
A
AAA circlerect
A belt connecting two 9-in-diameter drums on a conveyor system needs replacing. How many in long must
the belt be if the centers of the drums are 10 ft apart? Round to
tenths.
9 in9 in10 ft