# Examples for 8th grade - page 11

1. Bicycle wheel
A bicycle wheel has a diameter of 60 cm. Approximately how many times does wheel rotate at 2.5 km long trip?
2. Shelf
How many ways are there to arrange 6 books on a shelf?
3. Rhombus 2
Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long.
4. Tower
How many m2 of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°?
5. Profitable bank deposit 2012
Calculate the value of what money lose creditor with a deposit € 9500 for 4 years if the entire duration are interest 2.6% p.a. and tax on interest is 19% and annual inflation is 3.7% (Calculate what you will lose if you leave money lying idle at negative
6. Cube
The cube weighs 11 kg. How weight is cube of the same material, if its dimensions are 3-times smaller?
7. Equilateral triangle
How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it?
8. Hexagon A
Calculate area of regular hexagon inscribed in circle with radius r=9 cm.
9. Similarity coefficient
The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of ​​the larger triangle.
10. Metallurgical enterprise
Metallurgical company daily produces 318 tons of cast iron. How many tons of coke it burns to melt cast iron when 10 tons of cast consumes 6 tons of coke?
11. Balls
Three metal balls with volumes V1=71 cm3 V2=78 cm3 and V3=64 cm3 melted into one ball. Determine it's surface area.
12. Number ratio
Calculate two positive numbers that its ratio is 6:6 and difference was 0.
13. Plumber
Plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares so that no waste. Calculate the length of the sides of a square. How many squares cut it?
14. Team
The football team has 11 players. Their average age is 20 years. During the match due to injury, one player withdraws and the average age of the team is 18. How old was injured player?
Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B.
16. Diofant 2
Is equation ? solvable on the set of integers Z?
17. Speed of Slovakian trains
Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H
18. Right isosceles
Calculate area of the isosceles right triangle which perimeter is 41 cm.
19. Parquet floor
Three workers laid parquet floor for 2.301 hour. The first one would do this work alone 7 hours, the second in 6 hours. For how many hours would fulfill this work the third worker, if he worked alone?
20. Hole
In the center of the cube with edge 14 cm we will drill cylinder shape hole. Volume of the hole must be 27% of the cube. What drill diameter should be chosen?

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