Circle - problems

  1. Cutting square
    circle22 From a square with a side of 30 cm, we cut the circle with the highest possible diameter. How many percents of the square content is this circle?
  2. Cylinder height
    cylinder_9 Calculate the height of the cylinder and its surface is 2500 dm2 and the bases have a diameter 5dm.
  3. Hands
    soviet_watch The clock shows 12 hours. After how many minutes will agle between hour and minute hand 90°? Consider the continuous movement of both hands hours.
  4. Circle chord
    circleChord What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
  5. Rectangle
    rectangle_inscribed_circle The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
  6. Clock
    hodiny How many times a day hands on a clock overlap?
  7. 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.
  8. Washer
    pracka Washing machine drum wash at 55 RPM. Washing machine motor pulley has diameter 6 cm. What must be the diameter of the drum machine pulley when the motor is at 333 RPM?
  9. Square and circles
    kruznica_stvorec_1 Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
  10. Rectangle
    diagonal In rectangle with sides 3 and 10 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?
  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. 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.
  13. Cylinders
    cylinders Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
  14. Circle arc
    pizza Circle segment has a circumference of 72.95 cm and 1386.14 cm2 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. 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?
  17. Rhombus and inscribed circle
    rhombus_2 It is given a rhombus with side a = 75 cm and the radius of the inscribed circle r = 36 cm. Calculate the length of its two diagonals.
  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. Radians
    pi_text Convert 270° to radians. Write result as multiple of number π.
  20. 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.

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