1. Practice Quiz
Circles

2. A: Area A = πr2 Find the radius C: Circumference A: Area C = 2πr1
Find the area of a circle with circumference π.
A: Area
A = πr2
Find the radius
C: Circumference
A: Area
C = 2πr
A = πr2
π = 2πr

3. d: diameter r: radius d = 2r d = 8 d = 2 r = 4 r = 1 2
If the diameter of circle A is four times the diameter of circle B, what is the ratio of the
area of circle B to the area of circle A?
Step 1: Substitute integers for each diameter.
Find the radius for each circle.
d: diameter
r: radius
d = 2r
Circle A
Circle B
d = 8
d = 2
r = 4
r = 1

4. r = 4 r = 1 Area = πr2 Area = πr2 Area = π42 Area = π12 = π16 = 16π
If the diameter of circle A is four times the diameter of circle B, what is the ratio of the
area of circle B to the area of circle A?
Step 2: Find the area of each circle.
Circle A
Circle B
r = 4
r = 1
Area = πr2
Area = πr2
Area = π42
Area = π12
= π16
= 16π
= π1
= π
Step 3: Find the ratio.
= 1:16

5. d: diameter r: radius d = 2r d = 8 r = 4 C = 2πr A = πr2 = 2π4 = 8π3
If the diameter of circle is 8, what is the ratio between the circle’s area and its circumference?
d: diameter
r: radius
d = 2r
Step 1: Find the radius, given diameter is 8.
d = 8
r = 4
Step 2
Find circumference of circle.
Step 3
Find area of circle.
C = 2πr
A = πr2
= 2π4
= 8π
= π42
= π16
= 16π

6. C = 2πr A = πr2 = 2π4 = 8π = π42 = π16 = 16π = 2 = 2:1 3
If the diameter of circle is 8, what is the ratio between the circle’s area and its circumference?
Step 2
Find circumference of circle.
Step 3
Find area of circle.
C = 2πr
A = πr2
= 2π4
= 8π
= π42
= π16
= 16π
Step 4: Find ratio.
= 2
= 2:1

7. 4
On a farm, cylindrical silos are used to store wheat. If the circumference of a certain silo is 18 and the height is twice the diameter, what is the volume of wheat that can be stored in this solo?
Step 1
Find the radius.
Step 2
Find the diameter.
C = 2πr
d = 2r
18π = 2πr
d = 2(9) 9
d = 18
9 = r

8. r = 9 d = 18 36 V = πr2h h = 2d 9 V = π  92  36 h = 2(18)4
On a farm, cylindrical silos are used to store wheat. If the circumference of a certain silo is 18 and the height is twice the diameter, what is the volume of wheat that can be stored in this solo?
r = 9
d = 18
Step 3
Find the height.
Step 4
Find the volume. 36
V = πr2h
h = 2d 9
V = π  92  36
h = 2(18)
V = π  81  36
h = 36
V = 2916π

9. Volume V = πr2h Circumference C = 2πr V = 72π C = 2π  3 72π = πr2h5
If the volume of a cylinder is 72 and the height is 8, what is the circumference of the base?
Volume
V = πr2h
Circumference
C = 2πr
h =
V = 72π
C = 2π  3
72π = πr2h
C = 6π 
72π = πr28
72π = 8πr2
r = 3
9 = r2
Base is
grey circle
3 = r

10. C: Circumference C = 2πr A: Area Find the radius A = πr2 A = π6
Find the circumference of a circle with area π.
C: Circumference
C = 2πr
A: Area
Find the radius
A = πr2
A = π
C: Circumference
π = πr2
C = 2πr
C = 2π  1
C = 2π
1 = r2
1 = r

11. The circumference of a circle with a radius of 6 is how many times the circumference of a circle with a radius of 2? 7
C: Circumference
r = 6
Circle 1
r = 2
Circle 2
Answer
C = 2πr
C = 2πr
12π  4π
= 3
C = 2π  6
C = 2π  2
C = 12π
C = 4π

12. r = 4 r = 6 Let h = 2 V = 2(32π) V = πr2h V = 64π V = π  42  28
The two circular cylinders A and B have diameters of 8 and 12. If the volume of B is twice the volume of A, what is the ratio of the height of A to the height of B?
Cylinder A
Cylinder B
r = 4
r = 6
Let h = 2
V = 2(32π)
V = πr2h
V = 64π
V = π  42  2
V = πr2h
V = π  16  2
64π = π62h
V = π  32
64π = π36h
V = 32π
64π = 36πh

13. r = 4 r = 6 Let h = 2 Cylinder A Cylinder B 8
The two circular cylinders A and B have diameters of 8 and 12. If the volume of B is twice the volume of A, what is the ratio of the height of A to the height of B?
Cylinder A
Cylinder B
r = 4
r = 6
Let h = 2

14. 9
If a circle with an area of 4 is inscribed in a square , what is the perimeter of the square? 4
A: Area
P: Perimeter
A = 4π
P = 4s
A = πr2
d = 4
P = 4(4) 
r = 2
4π = πr2
P = 16
(Find radius)
4 = r2
2 = r

15. Square A: Area A = s2 A = 4 4 = s2 2 = s10
A square is inscribed in a circle. If the area of the square is 4, what is the ratio of the circumference of the circle to the area of the circle?
Square
Find hypotenuse
Use 45°-45°-90° Triangle
A: Area
A = s2 2
A = 4
4 = s2 2
2 = s

16. 6 Circle Square C: Circumference P: Perimeter C = 2πr  P = 4s11
In the figure, the circle inscribed inside the square has a radius of 3. What is the ratio of the perimeter of the square to the circumference of the circle? 6
Circle
Square
C: Circumference
P: Perimeter
d = 6
C = 2πr 
P = 4s
r = 3
C = 2π3
P = 4(6)
C = 6π
P = 24

17. 12
In the figure, the square is inscribed inside the circle. The circle has an area of 36. What is the length of the side of the square?
Pythagorean
Theorem
Circle Area
A = 36π
a2 + b2 = c2 s
A = πr2
s2 + s2 = 122 12
36π = πr2
2s2 = 144
36π πr2 π
s2 = 72 s
36 = r2
diameter = 2(radius)
6 = r
diameter = 2(6)
= 12

18. 13
In the figure, a circle is inscribed inside a square.
If the radius of the circle is , then what is the diagonal of the square? π π
d = π   π ? r
d = 2r

19. Circle Area 8 A = 16π A = πr2 16π = πr2  16π πr2 π 16 = r2 4 = r 14
The circle is inscribed inside the square. The circle has an area of 16. What is the length of diagonal AC?
Circle Area 8 B C
A = 16π
A = πr2
d = 8 
16π = πr2
r=4
16π πr2 π A D
16 = r2
4 = r

20. 14
The circle is inscribed inside the square. The circle has an area of 16. What is the length of diagonal AC? 8 B C 8  ? A D

21. Square Area Circle Area A = πr2 A = s2 A = 62 A = 36 A = π·9·2
In the figure, the square is inscribed inside the circle. The square has a side of 6. What is the area of the shaded region? 15
Square Area
Circle Area
A = πr2
A = s2 d
A = 62 6
A = 36 6
A = π·9·2
A = π·18
A = 18π

22. = Circle Area – Square Area
In the figure, the square is inscribed inside the circle. The square has a side of 6. What is the area of the shaded region? 15
Square Area
Circle Area
A = 36
A = 18π d 6
Area of shaded region 6
= Circle Area – Square Area
= 18π – 36

23. = Square Area – Circle Area
In the figure, the circle inscribed inside the square has a radius of 3. What is the area of the shaded region? 16 6
Circle Area
Square Area
A = πr2
A = s2
d = 6
A = π·32
A = 62  3
A = π·9
A = 36
A = 9π
Area of shaded region
= Square Area – Circle Area
= 36 – 9π

24. ABC = 48°. Find the measure of the major arc .17
Major Arc
in red
48
48
Major Arc
= 360 – 48
= 312

25. If , find the measure of CDE.18
= 60

26. In the figure, P, Q, and R lie on the same line
In the figure, P, Q, and R lie on the same line. P is the center of the larger circle, and Q is the center of the smaller circle. If the radius of the larger circle is 4,
what is the radius of the smaller circle? 19
Radius = 4
Radius = 2

27. Circumference of circle = 360°20
In the figure, square RSTU is inscribed in the circle. What is the degree measure of arc ?
Circumference
of circle = 360°

28. A square ABCD is inscribed in a circle of radius 8, as seen in the figure. What is the area of the shaded region? 21
Area of Circle
A = πr2 8
A = π  82
A = π  64
A = 64π

29. = 32π Area of Circle: A = 64π Area of Sector Central Angle = 180
A square ABCD is inscribed in a circle of radius 8, as seen in the figure. What is the area of the shaded region? 21
Area of Circle: A = 64π
Area of Sector 8
Central Angle
= 180
= 32π

30. 22
The circle has a diameter of 12. What is the length of ?
Length of major arc 6
C = 2πr
= 9π
C = 2π  6
= 12π

31. 23
If the circumference of the circle is 8, what is the area of the shaded region?
Circumference
Area of circle
C = 2πr
A = πr2
C = 8π
A = π  42
8π = 2πr
A = π  16
4 = r
Central Angle = 90°
A = 16π
Area of sector
= 4π

32. Square Circle A = πr2 A = s2 A = π(4.4)2 A = 8.82 A = π · 19.36
A semicircle is inscribed in a square in the figure. If a side of the square is 8.8 inches, what is the area, to the nearest integer, of the shaded region? 24
Square
Circle
A = πr2
8.8 in.
A = s2
A = π(4.4)2
A = 8.82
A = π · 19.36
A = 77.44
A = 19.36π
diameter = 8.8
radius = 4.4
A = 60.82
Semi-circle
Divide by 2
A = 30.41
Shaded Area
= Square Area – Circle Area
= – ≈ 47

33. In the figure, circles A, B, and C have radii 3, 5, and 7 respectively
In the figure, circles A, B, and C have radii 3, 5, and 7 respectively. What is the length of the perimeter of the triangle formed by joining the centers of the circles? 25 3 3 7 5 7 5
Perimeter =
= 30