1 / 33

Practice Quiz Circles

Practice calculating the area and circumference of circles with varying diameters and ratios in this quiz. Includes step-by-step solutions for circle-related math problems.

johnraymond
Download Presentation

Practice Quiz Circles

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Practice Quiz Circles

  2. 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

  3. 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? d: diameter r: radius Step 1: Substitute integers for each diameter. Find the radius for each circle. d = 2r Circle A Circle B d = 8 d = 2 r = 1 r = 4

  4. 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 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. 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 3 Find area of circle. Step 2 Find circumference of circle. C = 2πr A = πr2 = 2π4 = 8π = π16 = 16π = π42

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

  7. 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? 4 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. 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? 4 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. If the volume of a cylinder is 72 and the height is 8, what is the circumference of the base? 5 Volume Circumference V = πr2h C = 2πr C = 2π 3 h = V = 72π 72π= πr2h C = 6π  72π = πr28 72π = 8πr2 r = 3 9 = r2 Base is grey circle 3 = r

  10. 6 Find the circumference of a circle with area π. C = 2πr C: Circumference A: Area Find the radius A = πr2 C: Circumference A = π 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 Circle 1 Circle 2 r = 6 r = 2 Answer C = 2πr C = 2πr 12π 4π = 3 C = 2π 6 C = 2π 2 C = 12π C = 4π

  12. 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? 8 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. 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? 8 Cylinder A Cylinder B r = 4 r = 6 Let h = 2

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

  15. 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? 10 Square Find hypotenuse Use 45°-45°-90° Triangle A: Area A = s2 2 A = 4 4 = s2 2 2 = s

  16. 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? 11 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. 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? 12 Pythagorean Theorem Circle Area A = 36π a2 + b2 = c2 A = πr2 s2 + s2 = 122 s 12 36π= πr2 2s2 = 144 36ππr2 s2 = 72 s π π 36 = r2 diameter = 2(radius) 6 = r = 12 diameter = 2(6)

  18. 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? 13 π π d = π π   ? r d = 2r

  19. The circle is inscribed inside the square. The circle has an area of 16. What is the length of diagonal AC? 14 Circle Area 8 B C A = 16π A = πr2 d = 8 16π= πr2  r=4 16ππr2 A D 16 = r2 π π 4 = r

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

  21. 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. 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. 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 A = π·32 A = 62 d = 6  A = 36 3 A = π·9 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. 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. In the figure, square RSTU is inscribed in the circle. What is the degree measure of arc ? 20 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. 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. The circle has a diameter of 12. What is the length of ? 22 Length of major arc 6 C = 2πr = 9π C = 2π 6 = 12π

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

  32. 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 Circle Square A = πr2 A = s2 8.8 in. 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

  33. 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

More Related