# Examples for 8th grade - page 11

1. 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.
2. 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.
3. Number ratio Calculate two positive numbers that its ratio is 6:6 and difference was 0.
4. 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?
5. 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.
7. Diofant 2 Is equation ? solvable on the set of integers Z?
8. 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
9. Right isosceles Calculate area of the isosceles right triangle which perimeter is 41 cm.
10. 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?
11. Pool Mr. Peter build a pool shape of a four-sided prism with rhombus base in the garden. Base edge length is 8 m, distance of the opposite walls of the pool is 7 m. Estimated depth is 144 cm. How many hectoliters of water consume Mr. Peter to fill the pool?
12. 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?
13. Air Room is 35.6 m long, 19.6 dm wide and 591 cm high. How many people can simultaneously be in this room if for hygiene reasons is calculated 5000 dm3 of air per person?
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. Cu wire Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m3. Result round to one decimal place. Determine the radius of the circle, if its perimeter and area is the same number.
17. Discount Product has been discounted twice by 19%. What is the total discount given?
18. Seedcake Seedcake costs 44 cents. How many minimum seedcakes we must buy that we can pay in cash only whole euros?
19. Parallelogram Calculate area of the parallelogram ABCD as shown if |AB| = 19 cm, |BC| = 18 cm and angle BAD = 90°
20. Phone numbers How many 7-digit telephone numbers can be compiled from the digits 0,1,2,..,8,9 that no digit is repeated?

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