Right triangle + circular sector - practice problems
Number of problems found: 23
- Goat and circles
What is the radius of a circle centered on the other circle, and is the intersection of the two circles equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which - Field with vegetables
The field planted with vegetables has a rectangular isosceles triangle with a leg length of 24 m. At the triangle's vertices are rotating sprinklers with a range of 12 m. How much of the field sprinkler doesn't irrigated? - Circle section
An equilateral triangle with side 33 is an inscribed circle section whose center is in one of the triangle's vertices, and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio between the circumference to the circle sector a - Pendulum
Calculate the pendulum's length 2 cm lower in the lowest position than in the highest position. The circular arc length to be described when moving is 20cm.
- Diameter 5668
The span of the arc is 247 cm, and the height of the arc is 21.5 cm. What is the diameter of the circle? - Surface of the cone
Calculate the cone's surface if its height is 8 cm and the volume is 301.44 cm³. - Lunes of Hippocrates
Calculate the sum of the area of the so-called Hippocratic lunas, which were cut above the legs of a right triangle (a = 6cm, b = 8cm). Instructions: First, calculate the area of the semicircles above all sides of the ABC triangle. Compare the sum of the - Quarter circle
What is the radius of a circle inscribed in the quarter circle with a radius of 100 cm? - Spherical cap
The spherical cap has a base radius of 8 cm and a height of 5 cm. Calculate the radius of a sphere of which this spherical cap is cut.
- Flakes
A circle was inscribed in the square. We draw a semicircle above each side of the square as above the diameter. This resulted in four chips. Which is bigger: the area of the middle square or the area of the four chips? - Centimeter 5670
The tower of the Dean's Church in Ústí nad Labem deviates from the original vertical axis by 220 cm. Its original height was 48 m. At what height is the highest point of this tower now? Enter the result to the nearest centimeter. - The circle arc
Calculate the span of the arc, which is part of a circle with diameter d = 11 m and its height is 5 m. - Cone A2V
The cone's surface in the plane is a circular arc with a central angle of 126° and area 415 cm². Calculate the volume of a cone. - Maximum of volume
The shell of the cone is formed by winding a circular section with a radius of 1. For what central angle of a given circular section will the volume of the resulting cone be maximum?
- A spherical segment
The aspherical section, whose axial section has an angle of j = 120° in the center of the sphere, is part of a sphere with a radius r = 10 cm. Calculate the cut surface. - V-belt
Calculate the length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm (distance between pulley axes) - Horizontal Cylindrical Segment
How much fuel is in the horizontal cylindrical segment tank with a length of 10m, a width of level 1 meter, and a level is 0.2 meters below the tank's upper side? - Chord - TS
The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS? - Sphere parts, segment
A sphere with a diameter of 20.6 cm, the cut is a circle with a diameter of 16.2 cm. What are the volume of the segment and the surface of the segment?
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