Practice Quiz Circles

A: Area A = πr2 Find the radius C: Circumference A: Area C = 2πr 1 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

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

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

d: diameter r: radius d = 2r d = 8 r = 4 C = 2πr A = πr2 = 2π4 = 8π 3 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

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

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

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

Volume V = πr2h Circumference C = 2πr V = 72π C = 2π  3 72π = πr2h 5 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

C: Circumference C = 2πr A: Area Find the radius A = πr2 A = π 6 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

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

r = 4 r = 6 Let h = 2 V = 2(32π) V = πr2h V = 64π V = π  42  2 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 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

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

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

Square A: Area A = s2 A = 4 4 = s2 2 = s 10 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

6 Circle Square C: Circumference P: Perimeter C = 2πr  P = 4s 11 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

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

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

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

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

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

= 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

= 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

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

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

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

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°

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

= 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

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

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

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 = 77.44 – 30.41 ≈ 47

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 = 7 + 7 + 5 + 5 + 3 + 3 = 30