Area and Perimeter #3 (Circles) - LS Home Page

Circles page #1
Circumference of a Circle
The distance around a circle is its circumference.
C = πd or C = 2πr where π = 3.14
Example 1:
1. The approximate circumference:
7 cm
C = 3.14(14) = 43.96 cm.
2. The exact circumference:
C = 14 π
Example 2: A flagpole has a circumference of 30 cm. Find its diameter.
Use 3.14 for π.
C = πd
30 = 3.14d
30
3.14 = 3.14d
3.14
d = 9.6 cm.
Example 3: The sides of a square are 10 cm. Find the circumference of the
circumscribed circle.
10 cm
d
10 cm
d 2 = 10 2 +10 2
or
d 2 = 100 + 100
d 2 = 200
n 2
d = 200
d =10 2 d =10 2
n
n
Therefore, C = π10 2 = 10π 2

Problems:
Circles page #2
1. Find the exact circumference for each circle:
A. B.
5 cm
8 cm
2. To refinish a round table, a narrow strip of material is to be glued around the edge.
The table has a 42 inch diameter. How long must the strip be?
3. The rectangle is inscribed in the circle. Find the circumference of the circle.
30 cm
40 cm
4. What is the perimeter of an enclosed semicircular area where the radius of the
corresponding circle is 5? (Draw a sketch.)

Circles page #3
Example 4: Find the circumference of the circle whose center is (-2,1) and (2,4) is a
point on the circle.
r
4
3
We need to find the radius with the pythagorean
theorem or the distance formula.
r 2 = 3 2 + 4 2
r 2 = 9 +16
r 2 = 25
r = 5
r =
( 2 −−2) 2 + ( 4 −1) 2
r = ( 4 ) 2 + ( 3) 2
r = 16 +9
r = 25 = 5
The diameter is 2(5) = 10.
The circumference is 10 π.
Example 5: Find the circumference of the circle whose equation is (x-1) 2 +(y+2) 2 =16.
Remember: Equation of the circle: (x − h) 2 + (y − k) 2 = r 2
The center of our circle is (1,-2) and the radius is 4.
The diameter is 8.
The circumference is 8 π.
center: (h,k) radius = r
Problems:
1. Find the circumference of the circle whose center is (3,2) and (5,1) is a point on the
circle.
2. Find the circumference of the circle whose equation is (x-3) 2 +(y+5) 2 =36.

3. A gardener is fencing both sides of a circular walk around the garden shown. How
much fence does he need?
Walk
Circles page #4
Garden
3.5 feet
49 feet
Garden
4. Joe started jogging around a circular track. Halfway around he got tired and walked
back to his starting point. If the diameter of the track is 45 yards, how far did he go?
45 yards
start
5. The sides of a square are 6 cm. Find the circumference of the circumscribed circle.
6. The rectangle is inscribed in the circle. Find the circumference of the circle.
30°
2 cm

Circles page #5
Area of a Circle: A=πr 2
Example 1: Find the area of a circle with a radius of 6 cm.
A = πr 2 = π6 2 = 36 π cm 2
Example 2: The area of a circle is 70,650 in 2 . Find the radius to the nearest tenth of
an inch. Use 3.14 for π.
A = πr 2
70, 650 = 3.14r 2
70, 650
3.14 = 3.14r2
3.14
22,500 = r 2
r =
22,500 =150 inches
Example 3: Find the area of the shaded region:
4 cm
4 cm
3 cm
d 3 cm
d 2 = 3 2 + 4 2
d 2 = 9 + 16
d 2 = 25
d = 5
radius = 2.5 cm
Shaded Area = Area of the circle - Area of the rectangle
Shaded Area = (3.14)(2.5) 2 - (3)(4)
Shaded Area = 19.625 - 12
Shaded Area = 7.625 cm 2
Example 4: (x+3) 2 + (y-6) 2 = 16
A. Find the center of the circle. (-3,+6)
B. Find the radius of the circle. r = 4
C. Find the circumference of the circle. C = πd C = 8 π
D. Find the area of the circle. A = πr 2 A = 16 π

Problems:
Circles page #6
1. Find the area of a circle with a diameter of 6 cm.
2. The area of a circle is 1962.50 in 2 . Find the radius to the nearest tenth of an inch.
Use 3.14 for π.
3. Find the area of the shaded region:
8 cm
6 cm
4. (x+1) 2 + (y-8) 2 = 9
A. Find the center of the circle.
B. Find the radius of the circle.
C. Find the circumference of the circle.
D. Find the area of the circle.
5. Given the area of a circle, find the radius and diameter. Use 3.14 for π.
A = 380 cm 2
radius: _________
diameter: ________

Circles page #7
6. Find the shaded area to the nearest tenth of a centimeter:
A.The centers are O and P and the radius of the smaller circle is 4 cm. Use 3.14 for π.
O
P
B.
36 cm
25 cm
C. The square has a side of 4 inches and each circle has a radius of 1 inch.

7. (-1,-3) and (7,3) are the endpoints of a diameter of circle O.
A. Draw the circle:
Circles page #8
Find:
B. The center of the circle.
C. The radius of the circle.
D. The equation of the circle.
E. The circumference of the circle.
F. The area of the circle.
8. Given the area of the circle, find the circumference.
A = 16 π ft 2
Circumference = _______________
9. Given the circumference of the circle, find the area.
C = 12 π cm
Area = ________________
10. A pipe has a circumference of 78.5 cm. Find its diameter. Use 3.14 for π.