# Examples for 8th grade - page 33

1. Train from Brno First train started from Brno at 8 am at 60 km per hour. Second train started from Opava at 7 o'clock at the speed of 40 kilometers per hour. In how many hours and how far from cities trains meet when the distance of cities is 200 kilometers.
2. Mushrooms from the forest Magda and Tereza goes to pick mushrooms. Total found 70 mushrooms. Magda found that between fungi found 5/9 bedel. Tereza discovered that she found among fungi are 2/17 champignons. How many mushrooms found Magda?
3. Area 4gon Calculate area of 4-gon, two and the two sides are equal and parallel with lengths 11, 5, 11 and 5. Inner angles are 45°, 135°,45°, 135°.
4. 3sides prism The base of vertical prism is an isosceles triangle whose base is 10 cm and the arm is 13 cm long. Prism height is three times the height of base triangle. Calculate the surface area of the prism.
5. Squaring the Circle Calculating side of the square with the same area as the circle of radius 18.
6. Lathe Calculate the percentage of waste if the cube with 53 cm long edge is lathed to cylinder with a maximum volume.
7. The professor's birthday Professor of mathematics had 57 birthdays. The director congratulated him. The professor asked the director: "And how old are you?" The director replied: "I'm exactly twice as many years than you were when I was old as to you today." How old is the direc
8. Skier At this point, the first skier lead 20 km before the second skier and travels at a constant speed 19 km/h. The second skier rides at 24 km/h. How long take him to catch up the first?
9. Cube wall Calculate the cube's diagonal diagonal if you know that the surface of one wall is equal to 36 centimeters square. Please also calculate its volume.
10. ISO Triangle V2 Perimeter of RR triangle (isosceles) is 474 m and the base is 48 m longer than the arms. Calculate the area of this triangle.
11. Triangle Calculate heights of the triangle ABC if sides of the triangle are a=75, b=84 and c=33.
12. Bricks Openings in perforated bricks occupy 10% and brick has dimensions 30 cm, 15 cm and 7.5 cm. Calculate a) the weight of a perforated bricks, if you know that the density of the full brick material is p = 1800 kg/m3 (1.8 kg/dm3) b) the number of perforated. Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall?
14. Carbon dioxide Calculate how many grams of oxygen are in 50 g of carbon dioxide CO2. Relative atomic mass of oxygen is 16 and of carbon is 12.
15. Similarity of squares The ratio of the similarity of the squares ABCD and KLMN is 2.5. Square KLMN area is greater than area of a square ABCD with side a: ?
16. Again saw From the trunk of the tree we have to a sculpture beam with rectangular cross-section with dimensions 146 mm and 128 mm. What is the trunk smallest diameter?
17. Pumps 3 Two pumps of the same power fill the garden pool for 10 hours. How many of these pumps would have to use if we want to shorten the filling of the pool to four hours?
18. Clock What distance will pass end of 8 cm long hour hand for 15 minutes?
19. Gon functions Decide which of the numbers (values ​​of trigonometric functions) are positive and which are negative (or zero). Positive mark +1 and negative -1. 8.3 meters long ladder is leaning against the wall of the well, and its lower end is 1.2 meters from this wall. How high from the bottom of a well is the top edge of the ladder?