Circle - problems

  1. Hypotenuse - RT
    triangle_bac_1 A triangle has a hypotenuse of 55 and an altitude to the hypotenuse of 33. What is the area of the triangle?
  2. A cylinder
    string A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?
  3. Water flow 2
    water3_9 How many litres of water will flow in 7 minutes from a cylindrical pipe 1 cm in diameter, if the water flows at a speed of 30 km per hour
  4. A bridge
    arc123 A bridge over a river is in the shape of the arc of a circle with each base of the bridge at the river's edge. At the center of the river, the bridge is 10 feet above the water. At 27 feet from the edge of the river, the bridge is 9 feet above the water. H
  5. Ruler and compass
    triangle_bac Use a ruler and compass to construct a triangle ABC with AB 5cm BAC 60° and ACB 45°.
  6. 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.
  7. 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?
  8. Clock
    hodiny How many times a day hands on a clock overlap?
  9. Rectangle
    rectangle_inscribed_circle The rectangle is 31 cm long and 28 cm wide. Determine the radius of the circle circumscribing rectangle.
  10. Washer
    pracka Washing machine drum wash at 54 RPM. Washing machine motor pulley has diameter 5 cm. What must be the diameter of the drum machine pulley when the motor is at 301 RPM?
  11. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 dm2. Calculate the volume of a cone.
  12. Square and circles
    kruznica_stvorec_1 Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
  13. 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?
  14. Circles
    two_circles The areas of the two circles are in the ratio 2:14. The larger circle has diameter 14. Calculate the radius of the smaller circle.
  15. Cylinders
    cylinders Area of the side of two cylinders is same rectangle of 12 mm × 19 mm. Which cylinder has a larger volume and by how much?
  16. Circle arc
    pizza Circle segment has a circumference of 41.89 m and 251.33 m2 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 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
  19. 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.
  20. Cone
    cones Circular cone of height 15 cm and volume 10598 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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