Circle + reason - practice problems
Number of problems found: 57
- Diameter 4111
How many balls with a diameter of 3.25 cm with a mixture in a circle with a diameter of 27 cm? - Intersections
How many intersections have circles with radius 16 mm and 15 mm if the distance of their centers is 16 mm? - Velocipede
The front wheel of the velocipede from the year 1880 had a diameter 1.8 m. Suppose the front wheel is turned again once, then the rear wheel six times. What was the diameter of the rear wheel? - Saw
Imagine that the saw blade with a diameter 40 cm has one tooth-colored with a different color. How long does the tooth's tip describe the path after 15 minutes if the blade is rotated 13365 times? - Gear
Two gears fit into each other and have a transfer of 2:3. Centers of gears are spaced 82 cm. What are the radii of the gears? - Washer
The washing machine drum washes at 71 RPM. The washing machine motor pulley has a diameter of 8 cm. What must be the diameter of the drum machine pulley when the motor is at 351 RPM? - Equator
Suppose that a tourist went on foot over the Globe equator. How many meters more track made his hat on his head as the shoes on your feet? The radius of the Earth is $R km, and the height of the tourist is $v m. - Distinguished 37083
Three circles of the same size are drawn on the playing field. Arrange the 16 pins so that there are 9 pins in each circle. Find at least eight significantly different layouts, i.e. J. such layouts in which pins or circles are not distinguished. - Smaller 4835
There are two gears in the wall clock. The larger wheel has 54 teeth and the smaller 24 teeth. How many times does the small wheel turn if the big one turns four times? - Snowman
In a circle with a diameter of 40 cm are drawn three circles (as a snowman) where: its diameters are integers, each larger circle diameter is 2 cm larger than the diameter of the previous circle. Determine snowman height if we wish for the highest snowman - Snowman 2
On the medal, which has the shape of a circle with a diameter 18 cm, is sketched a snowman so that the following requirements are met: 1. snowman is composed of three circles, 2. space over the snowman is the same as under it, 3. diameters of all circles - Simultaneously 6997
Two boys train to run on a 400 m closed track. They both run simultaneously from the same starting track in the same direction. Boy A runs at a constant speed of 5 m/s, and Boy B runs at a constant speed of 3 m/s. At what time does Boy A overtake Boy B fo - Wiring
The conduit has a cross-section 54² mm. Maybe put it into 6 conductors with a cross section S2 $mm²? - Lake or pond
The landlord has a square lake. Trees grow around this lake. The lake wants to enlarge the pond twice and not cut down or flood any trees. How will he do that? - Inscribed 44101
A circle is inscribed in the triangle with sides of 13 cm, 14 cm, and 15 cm. What is its radius? - Circles
Three circles of radius 30 cm, 28 cm, and 37 cm are mutually tangent. What is the triangle perimeter whose vertices are the circles' centers? - Coin
How many 20-cent coins must be put in a row that the next 20-cent coins after them (above) rolled on its axis? - Z9–I–1
In all nine fields of given shape to be filled with natural numbers so that: • each of the numbers 2, 4, 6, and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in th - Quatrefoil 81138
Gothic quatrefoil is an ornament in which four identical touching smaller circles are inscribed in a larger circle, as you can see in the picture. The radius of the great circle is one meter. Calculate the radius of the smaller circle in meters. - Circumscribing 80498
Given is an acute-angled triangle ABC. On the half lines opposite to BA and CA lie successively the points D and E such that |BD| = |AC| and |CE| = |AB|. Prove that the center of the circle circumscribing triangle ADE lies on the circle circumscribing tri
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