# Circle + area of shape - examples

1. Masquerade ball Marie wants to make a cone-shaped witch's hat for a masquerade ball. How much material will it need if it counts on an annular rim with diameters of 28cm and 44cm? Hat side length is 30cm. Add 5% of the material to the bust. Round to cm2.
2. Rectangle In rectangle with sides 10 and 8 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?
3. Circles The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
4. Cylinders 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?
5. Circle arc Circle segment has a circumference of 72.95 cm and 1386.14 cm2 area. Calculate the radius of the circle and size of central angle.
6. Circular pool The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
7. Described Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
8. Arc and segment Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 33 and corresponding angle is ?.
9. Pizza Pizza with a diameter 50 cm have weight 559 g. What diameter will have a pizza weighing 855 g if it is make from the same cloth (same thickness....) and same decorated?
10. Roller Cylinder shell has the same content as one of its base. Cylinder height is 15 dm. What is the radius of the base of the cylinder?
11. Hexagon A Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
12. Circle How big is area of circle if its circumference is 80.6 cm?
13. Axial section Axial section of the cylinder has a diagonal 31 cm long and we know that the area of the side and the area of base is in ratio 3:2. Calculate the height and radius of the cylinder base.
14. Tinsmith Tinsmith construct chimney pipe 145 cm long and 15 cm wide. What are the dimensions of the sheet will have to prepare for the construction of a pipe when the plate overlap at the joint add \$x cm width of the plate?
15. Radius Determine the radius of the circle, if its perimeter and area is the same number.
16. Wire One pull of wire is reduced its diameter by 14%. What will be diameter of wire with diameter 19 mm over 10 pulls?
17. Goat and circles What is the radius of a circle centered on the other circle and the intersection of the two circles is 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 g
18. Circle and angle What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad?
19. Posters Column with posters in the form of a cylinder is 2 m high and its diameter is 1.7 m. What is the content area for which it is possible to stick posters?
20. Wiring Conduit has a cross section 482 mm. Maybe put it into 6 conductors with a cross section S2 \$mm2?

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