# Circle + length - examples

1. Cube into cylinder
If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
2. Hands
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.
3. Rectangle
The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
4. Clock
How many times a day hands on a clock overlap?
5. Washer
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?
6. Circle arc
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.
7. Cone
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.
8. Earth parallel
Earth's radius is 6374 km long. Calculate the length parallel of latitude 70°.
9. Described
Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
10. Quarter circular
The wire that is hooked around the perimeter of quarter-circular arc has length 3π+12. Determine the radius of circle arc.
11. Cap
Jesters hat is shaped a rotating cone. Calculate how much paper is needed to the cap 60 cm high when head circumference is 52 cm.
12. Bicycle wheel
Bicycle wheel has a diameter of 70 cm. Approximately how many times the wheel rotates at 4.7 km long trip?
13. Cu wire
Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m3. Result round to one decimal place.
14. Cylinder
Calculate the dimensions of rotating cylindrical container with volume 2 l, if height of container is equal to the diameter of the base.
15. Clocks
How long path will walk the end of the clock's minute-hand long 7 cm for 330 minutes? How long will walk in the same time hour-hand?
16. Estate
Semicircle estate must be fence. The straight section has 26 meters long fence. How many meters of fence should buy?
17. Track arc
Two straight tracks is in an angle 74°. They will join with circular arc with radius r=1127 m. How long will be arc connecting these lines (L)? How far is the center point of arc from track crossings (x)?
18. Wire D
Wire length 1 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle.
19. Park
In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m.
20. Rail turn
The curve radius on the railway line is 532 m . Length of rail track on it is 818 m. How many degrees is the angle ASB, if A and B are boundary points and S is center of arc curve.

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