Circular sector practice problems - page 3 of 4
Direction: Solve each problem carefully and show your solution in each item.Number of problems found: 72
- 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 - Circular sector
I have a circular sector with a length of 15 cm with an unknown central angle. It is created from a circle with a radius of 5 cm. What is the central angle alpha in the circular sector? - Circular arc
Calculate the center angle and length of the circular arc if the radius r = 21 cm and the area of the slice is 328.5 cm² - 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? - Circular segment
What is the radius of a circular section whose central angle is 36° and the area of S = 53.095 cm²? - Semicircle
The ornament consists of one square and four dark semicircles. The area of the square is 4 cm². Find the area of one dark semicircle and round the result to hundreds. - The tower
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. - Goat
The fenced flower bed has the shape of a regular hexagon. The tops are formed by fence posts. The fence around the flowerbed measures 60 m. A goat is tied to one of the pillars from the outside and grazes on the surrounding meadow (the goat should not ent - A goat
In the square garden of side (a), a goat is tied in the middle of one side. Calculate the length of the rope (r) so that the goat grazes exactly half the garden. If r = c * a, find the constant c. - Circumferential 8399
A circle with a radius r=8 cm is divided by points K and L in a ratio of 5 to 4. Calculate the sizes of the center and circumferential angles, corresponding to both arcs and the area of the larger segment. - 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 isn't irrigated? - Equilateral triangle v3
Find the area of the colored gray part. An equilateral triangle has a side length of 8 cm. Arc centers are the vertices of a triangle. - 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 - Automatic 45711
What grass area can the automatic sprayer spray if it is set to spray at an angle of 120 ° and the water sprays up to a maximum distance of 5 meters? - Circle segment A quarter circle with a radius of 4 has the same area as a circle segment with a radius of 3. What is the magnitude of the center angle of the circle segment?
- Mice
Mice consumed a circular hole in a slice of cheese. The cheese is a circular cut with a radius of 20 cm and an angle of 90 degrees. What percentage of the cheese ate mice if they made 20 holes with a diameter of 2 cm? - Determine 8010
Determine the cone's base's radius if its shell develops into a circular section with radius "s" = 10 and center angle x = 60 °. r = ?, o =? - Spherical sector
The spherical sector has axial section has an angle of α = 120° in the center of the sphere, is part of a sphere with a radius r = 10 cm. Calculate the surface of this spherical sector. - Angle of the sector
Find the angle of the sector of a circle radius of 20 units where the area is equal to the lateral area of a cone with a radius of 8 units.
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