Circle - 8th grade (13y) - math problems

  1. Two chords
    tetivy Calculate the length of chord AB and perpendicular chord BC to circle if AB is 4 cm from the center of the circle and BC 8 cm from the center of the circle.
  2. The cylinder 2
    cylinder Find the volume and the lateral area of a cylinder of height 12 inches and a base radius of 4 inches.
  3. Company logo
    circle_square_insribed The company logo consists of a blue circle with a radius of 4 cm, which is an inscribed white square. What is the area of the blue part of the logo?
  4. Hands
    soviet_watch The clock shows 12 hours. After how many minutes will angle between the hour and minute hand 90°? Consider the continuous movement of both hands hours.
  5. Circle chord
    circleChord What is the length d of the chord circle of diameter 50 dm, if the distance from the center circle is 21 dm?
  6. Rectangle
    rectangle_inscribed_circle The rectangle is 21 cm long and 38 cm wide. Determine the radius of the circle circumscribing rectangle.
  7. Clock
    hodiny How many times a day hands on a clock overlap?
  8. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
  9. Rectangle
    diagonal In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
  10. Square and circles
    kruznica_stvorec_1 Square with sides 83 cm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
  11. Circles
    two_circles The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
  12. Cylinders
    cylinders Area of the side of two cylinders is same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume and by how much?
  13. MO SK/CZ Z9–I–3
    ball_floating_water John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
  14. Circle arc
    pizza Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of central angle.
  15. Rhombus
    rhomus_circle It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
  16. Rhombus and inscribed circle
    rhombus_2 It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
  17. Gear
    ozubene_kolesa Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
  18. Cone
    cones Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
  19. Tangents
    tangents To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre.
  20. Radians
    pi_text Convert 270° to radians. Write result as multiple of number π.

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