# Examples for 8th grade - page 53

1. Square circles Calculate the length of the described and inscribed circle to the square ABCD with a side of 5cm.
2. Obtuse angle The line OH is the height of the triangle DOM, line MN is the bisector of angle DMO. obtuse angle between the lines MN and OH is four times larger than the angle DMN. What size is the angle DMO? (see attached image)
3. Three men Alex is half younger than Jan, which is one-third younger than George. The sum of their ages is 48. How are these three men old?
4. Pool Pool is filled with two water supply. The first supply fill pool for nine hours, the second for six hours. How many hours will take fill the pool when the water flows in through the first supply 3 hours and then we will open a second supply?
5. Isosceles trapezoid What is the height of an isosceles trapezoid, the base of which has a length of 11 cm and 8 cm and whose legs measure 2.5 cm?
6. Laths There are two laths in the garage opposite one another: one 2 meters long and the other 3 meters long. They fall against each other and lean against the opposite walls of the garage both laths and touch at a height of 70 cm above the garage floor. How wide
7. Average height In a class are 34 students. The average height of students is 165 cm. What will be the average height of students in the classroom when two pupils tall 176 cm and 170 cm moved from this school/class?
8. Tray Wjat height reach water level in the tray shaped a cuboid, if it is 420 liters of water and bottom dimensions are 120 cm and 70 cm.
9. The city In the city is 2/4 of women married to 3/4 men. What percentage of townspeople is single (not married)?
10. Painting To paint the pool with dimensions: 2 meters depth, 3m x 4m we bought paint to 50 meters square. How many "paint" will be a waste?
11. Mr. John Mr. John wants to buy winter apples Spartan. There are two ways to buy: 1) buy apples at the marketplace, where 1 kg costs 15 CZK. 2) Bring the car to the agricultural farm, where the apples are sold after 9 CZK per kilogram. However, he must pay CZK 150.
12. Welders Welder do the job for six hours, the second one for 8 hours. How long do the job third welder if all together can do job in 2 hours?
13. Sputnik The first Earth satellite was flying at speed 8000 m/s. At that rate he circled the earth in 82 minutes. Jet flies at an average speed 800 km/h. How long would it take circle the earth round?
14. Number What number is 20 % smaller than the number 198?
15. The creek Workers cleaned the creek within 3 days. The first day cleanse one-fifth the length of the creek, the next day 40% of the length of the stream and the third day 8 km length of the creek. How long is a creek?
16. Juice box 2 Box with juice has the shape of a cuboid. Internal dimensions are 15 cm, 20 cm and 32 cm. If the box stay at the smallest base juice level reaches 4 cm below the upper base. How much internal volume of the box fills juice? How many cm below the top of the
17. James James paints a fence. If every day instead of 14 planks painted 16 would be done on one day earlier. How many of planks has a fence altogether?
18. Saw Blade circular saw with a diameter 42 cm turns 825 times per minute. Expresses his cutting speed in meters per minute.
19. Prism The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters?
20. Water well Drilled well has a depth 20 meters and 0.1 meters radius. How many liters of water can fit into the well?

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