# Examples for secondary school students - page 7

1. Prism X The prism with the edges of the lengths x cm, 2x cm and 3x cm has volume 20250 cm3. What is the area of surface of the prism?
2. Pyramid roof 2/4 of area of ​​the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered?
3. Inflation Once upon a time, tsar owned a money printer and printed and printed. The result of printing money prices went up,in the first year 3.9 %, in the second 6%, in the third 4.7% and in the fourth 5.5%. Then tsar was failed in election. Calculate the aver
4. Train and car The train and the car started at a constant speed to journey. When the train travels 87 km, the car travels 97 km. How many km travels the train when the car travels 87 km?
5. Camel Camel owner wants to get out of the city into oasis. He bought 3000 bananas, which wants to sell in oasis. However oasis from the city divided 1,000 kilometers of desert. Camel can carry at one time up to 1000 bananas, and for every kilometer traveled, ea
6. Negative percentage In 2004, the company had a loss of 40900 Euros. Two years later he was already in profit 48900 Eur. Calculate what percentage of the company increased profits in this two years.
7. Hexagon There is regular hexagon ABCDEF. If area of the triangle ABC is 22, what is area of the hexagon ABCDEF? I do not know how to solve it simply....
8. Rotation of the Earth Calculate the circumferential speed of the Earth's surface at a latitude of 61°​​. Consider a globe with a radius of 6378 km.
9. Rates When gas consumption, the consumer may choose one of two rates: rate A - which pays 0.4 € per 1 m3 of gas a flat monthly fee of 3.9 € (regardless of consumption) rate B - which pays 0.359 € per 1 m3 of gas a flat monthly fee of 12.5 € From what monthl
10. Plastic pipe Calculate weight of the plastic pipe with diameter d = 70 mm and length 380 cm if the wall thickness is 4 mm and the density of plastic is 1367 kg/m3.
11. Cube - angles Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
12. Tetrahedral pyramid Calculate the volume and surface area of a regular tetrahedral pyramid, its height is \$b cm and the length of the edges of the base is 6 cm.
13. Sphere slices Calculate volume and surface of a sphere, if the radii of parallel cuts r1=31 cm, r2=92 cm and its distance v=25 cm.
14. Triangle SSS Calculate perimeter and area of ​​a triangle ABC, if a=42, b=57 and c=42.
15. Climb On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went?
16. ISO triangle Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm.
17. Rotary cone The volume of the rotation of the cone is 472 cm3 and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone.
18. Triangular prism Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.
19. Cone Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume.
20. Tourists From the cottage started first group of tourists at 10:00 AM at speed 4 km/h. The second started after them 47 minutes later at speed 6 km/h. How long and how many kilometers from the cottage will catch the first group?

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