Circle - examples
- A pipe
A radius of a cylindrical pipe is 2 ft. If the pipe is 17 ft long, what is its volume?
- Two chords
There is a given circle k (center S, radius r). From point A which lies on circle k are starting two chords of length r. What angle does chords make? Draw and measure.
Prove that k1 and k2 is the equations of two circles. Find the equation of the line that passes through the centers of these circles. k1: x2+y2+2x+4y+1=0 k2: x2+y2-8x+6y+9=0
- The big clock
The big clock hands stopped at a random moment. What is the probability that: a) a small hand showed the time between 1:00 and 3:00? b) the big hand was in the same area as a small hand in the role of a)? c) did the hours just show the time between 21:00.
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.
- Circle chord
What is the length d of the chord circle of diameter 36 m, if distance from the center circle is 16 m?
The rectangle is 11 cm long and 45 cm wide. Determine the radius of the circle circumscribing rectangle.
How many times a day hands on a clock overlap?
- Cone A2V
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.
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?
- Square and circles
Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
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?
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.
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?
- MO SK/CZ Z9–I–3
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.
- Circle arc
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.
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.
Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
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.
- Rhombus and inscribed
Rhombus has side a = 42 cm, the radius of the inscribed circle is r = 18 cm. Calculate the length of its two diagonals.