# Grade - examples - page 30

Average climb of the road is given by ratio 1:15. By what angle road average climb?
2. Fractions
Sort fractions ? by its size. Result write as three serial numbers 1,2,3.
3. Hexagon
Draw a regular hexagon inscribed in a circle with radius r=8 cm. What is its perimeter?
4. Pizza master
Master says that he can splits pizza to 16 parts by five equals straight cuts. Is it possible?
5. Lid
What is the weight of concrete cover (lid) to round shape well with a diameter 1.8 m, if the thickness of the cover is 11 cm? 1 m3 of concrete weighs 2190 kg.
6. Elevation
What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
7. Dices
We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
8. Lines
Five bus lines runs at intervals 3, 6, 9, 12, 15 minutes. In the morning, suddenly start at 4:00. After how many minutes the bus lines meet again?
9. Triangle and its heights
Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
10. Fertilizer
Mr. Gherkin use for fertilization 8% solution of fertilizer. 4 liters of it still left. How much water must be added to the solution to make only 4% solution?
11. N-gon
How many diagonals has convex 11-gon?
12. Circular sector
I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector?
13. Working time - shortening
The media often speculates about the change (especially to shorten) the working time of the five-day eight-hour working week to another working model. Calculate how many hours a day the employee would have to work a day at 3-day work week if he must work t
14. Cinema
Cinema auditorium is built for 3300 people. The first row is planned for 36 seats and each next gradually 4 more. How many rows of seats will have auditorium?
15. Euclid2
In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
16. Denominator
Calculate the missing denominator x: ?
17. Pedestrian and cyclist
Pedestrian out with a speed of 4 km/hour from city center and after 1hour and 10 minutes came after him cyclist at speed of 18 km/h. At how many minutes he catches up with pedestrian?
18. Tiles
Hall has dimensions 325 &time; 170 dm. What is the largest size of square tiles that can be entire hall tiled and how many we need them?
19. Circle in rhombus
In the rhombus is inscribed circle. Contact points of touch divide the sides to parts of length 19 cm and 6 cm. Calculate the circle area.
20. Sea
How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km).

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