Circle - problems

  1. Equation of circle 2
    circle_axes Find the equation of a circle which touches the axis of y at a distance 4 from the origin and cuts off an intercept of length 6 on the axis x.
  2. Pendulum
    kyvadlo Calculate the length of the pendulum that is 2 cm lower in the lowest position than in the highest position. The length of the circular arc to be described when moving is 20cm.
  3. Clock hands
    clocks2_16 The second hand has a length of 1.5 cm. How long does the endpoint of this hand travel in one day?
  4. Tangent 3
    tangetns In a circle with centre O radius is 4√5 cm. EC is the tangent to the circle at point D. Segment AB IS THE DIAMETER of given circle. POINT A is joined with POINT E and POINT B is joined with POINT C. Find DC if BC IS 8cm.
  5. Cylinder horizontally
    CylindricalSegment_1000 The cylinder with a diameter of 3 m and a height/length of 15 m is laid horizontally. Water is poured into it, reaching a height of 60 cm below the axis of the cylinder. How many hectoliters of water is in the cylinder?
  6. Hands
    soviet_watch The clock shows 12 hours. After how many minutes will agle between hour and minute hand 80°? Consider the continuous movement of both hands hours.
  7. Circle chord
    circleChord What is the length d of the chord circle of diameter 58 mm, if distance from the center circle is 24 mm?
  8. Clock
    hodiny How many times a day hands on a clock overlap?
  9. Rectangle
    rectangle_inscribed_circle The rectangle is 28 cm long and 21 cm wide. Determine the radius of the circle circumscribing rectangle.
  10. Washer
    pracka Washing machine drum wash at 75 RPM. Washing machine motor pulley has diameter 6 cm. What must be the diameter of the drum machine pulley when the motor is at 316 RPM?
  11. 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.
  12. Square and circles
    kruznica_stvorec_1 Square with sides 89 m is circumscribed and inscribed with circles. Determine the radiuses of both circles.
  13. Rectangle
    diagonal In rectangle with sides 10 and 9 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?
  14. Circles
    two_circles The areas of the two circles are in the ratio 1:15. The larger circle has diameter 25. Calculate the radius of the smaller circle.
  15. Cylinders
    cylinders Area of the side of two cylinders is same rectangle of 45 cm × 32 cm. Which cylinder has a larger volume and by how much?
  16. Circle arc
    pizza Circle segment has a circumference of 13.26 mm and 252.03 mm2 area. Calculate the radius of the circle and size of central angle.
  17. 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.
  18. Gear
    ozubene_kolesa Two gears, fit into each other, has transfer 1:5. Centres of gears are spaced 28 cm. What are the radii of the gears?
  19. Rhombus
    rhomus_circle It is given a rhombus of side length a = 11 cm. Touch points of inscribed circle divided his sides into sections a1 = 6 cm and a2 = 5 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
  20. Cone
    cones Circular cone of height 16 cm and volume 5024 cm3 is at third of the height (measured from the bottom) cut plane parallel to base. Calculate the radius and circumference of the circular cut.

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