# Circle + length - math problems

1. Circle and square An ABCD square with a side length of 100 mm is given. Calculate the radius of the circle that passes through the vertices B, C and the center of the side AD.
2. Length of the arc What is the length of the arc of a circle k (S, r=68mm), which belongs to a central angle of 78°?
3. Winch drum Originally an empty winch drum with a diameter of 20 cm and a width of 30 cm on the rescue car, he started winding a rope with a thickness of 1 cm beautifully from edge to edge. The winch stopped after 80 turns. It remains to spin 3.54m of rope (without h
4. Suppose Suppose you know that the length of a line segment is 15, x2=6, y2=14 and x1= -3. Find the possible value of y1. Is there more than one possible answer? Why or why not?
5. A cell tower A cell tower is located at coordinates (-5, -7) and has a circular range of 12 units. If Mr. XYZ is located at coordinates (4,5), will he be able to get a signal?
6. Two chords In a circle with radius r = 26 cm two parallel chords are drawn. One chord has a length t1 = 48 cm and the second has a length t2 = 20 cm, with the center lying between them. Calculate the distance of two chords.
7. Rotaty motion What is the minimum speed and frequency that we need to rotate with water can in a vertical plane along a circle with a radius of 70 cm to prevent water from spilling?
8. Construct rhombus Construct rhombus ABCD if given diagonal length | AC | = 8cm, inscribed circle radius r = 1.5cm
9. Parallels and one secant There are two different parallel lines a, b and a line c that intersect the two parallel lines. Draw a circle that touches all lines at the same time.
10. Two chords 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. Calculate the radius of the circle whose length is 107 cm larger than its diameter
12. Tree trunk What is the smallest diameter of a tree trunk that we can cut a square-section square with a side length of 20 cm? Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? Hat side length is 30cm. Add 5% of the material to the bust. Round to cm2.
14. 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?
15. Velocipedes In the 19th century, bicycles did not have a chain drive, and the pedals were connected directly to the wheel axis. This wheel diameter gradually increased until the so-called high bicycles (velocipedes) with a front wheel diameter of up to 1.5 meters, wh
16. Diameter of a cylinder The diameter of the cylinder is 42 cm. How many times does the cylinder turn on a 66m long track?
17. Two gears The two gears fit together. The larger gear has 32 teeth, the smaller has 20 teeth less. How many times does turn a smaller gear if the bigger gear turns three times?
18. Iron density Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3.
19. Distance problem A=(x, x) B=(1,4) Distance AB=√5, find x;
20. 3d printer 3D printing ABS filament with diameter 1.75 mm has density 1.04 g/cm3. Find the length of m = 5 kg spool filament. (how to calculate length)

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