# Circle + angle - math problems

#### Number of problems found: 106

• Sphere in cone
A sphere is inscribed in the cone (the intersection of their boundaries consists of a circle and one point). The ratio of the surface of the ball and the contents of the base is 4: 3. A plane passing through the axis of a cone cuts the cone in an isoscele
Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.
• Dodecagon
Calculate the size of the smaller of the angles determined by lines A1 A4 and A2 A10 in the regular dodecagon A1A2A3. .. A12. Express the result in degrees.
• Coordinates hexagon
The regular hexagon ABCDEF is given. Point A has coordinates [1; 3] and point D has coordinates [4; 7]. Calculate the sum of the coordinates of the center of its described circle.
• Annulus
Two concentric circles with radii 1 and 9 surround the annular circle. This ring is inscribed with n circles that do not overlap. Determine the highest possible value of n.
• Hexa pyramid
The base of the regular pyramid is a hexagon, which can be described by a circle with a radius of 1 m. Find the volume of the pyramid 2.5 m high.
• Eq triangle minus arcs
In an equilateral triangle with a 2cm side, the arcs of three circles are drawn from the centers at the vertices and radii 1cm. Calculate the content of the shaded part - a formation that makes up the difference between the triangle area and circular cuts
• Circular railway
The railway is to interconnect in a circular arc the points A, B, and C, whose distances are | AB | = 30 km, AC = 95 km, BC | = 70 km. How long will the track from A to C?
• Coal mine
The towing wheel has a diameter of 1.7 meters. How many meters does the elevator cage lower when the wheel turns 32 times?
• RPM
An electric motor makes 3,000 revolutions per minutes. How many degrees does it rotate in one second?
• Hexagon in circle
Calculate the radius of a circle whose length is 10 cm greater than the circumference of a regular hexagon inscribed in this circle.
• RT - inscribed circle
In a rectangular triangle has sides lengths> a = 30cm, b = 12.5cm. The right angle is at the vertex C. Calculate the radius of the inscribed circle.
• Construct
Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description.
• Diagonals of pentagon
Calculate the diagonal length of the regular pentagon: a) inscribed in a circle of radius 12dm; b) a circumscribed circle with a radius of 12dm.
• Special watch
Fero bought a special watch on the market. They have only one (minute) hand and a display that shows which angle between the hour and minute hand. How many hours it was when his watch showed - the minute hand points to number 2; the display shows 125°?
• Decagon
Calculate the area and circumference of the regular decagon when its radius of a circle circumscribing is R = 1m
• Nonagon
Calculate the area and perimeter of a regular nonagon if its radius of inscribed circle is r = 10cm
• Irrigation sprinkler
The irrigation sprinkler can twist with an angle of 320° and has a reach of 12 meters. Which area can irrigate?
• 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.
• 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

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