# Examples for secondary school students - page 7

1. 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?
2. 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
3. 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.
4. 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.
5. 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
6. 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....
7. Cube - angles
Calculate angle between the wall diagonal and cube base. Calculate the angle between the cube body diagonal and cube base.
8. 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.
9. 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.
10. 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.
11. Triangle SSS
Calculate perimeter and area of ​​a triangle ABC, if a=40, b=36 and c=36.
12. 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?
13. 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.
14. 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.
15. 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.
16. 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.
17. 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?
18. Recursion squares
In the square ABCD is inscribed a square so that its vertices lie at the centers of the sides of the square ABCD.The procedure of inscribing square is repeated this way. Side length of square ABCD is a = 22 cm. Calculate: a) the sum of perimeters of all
19. Roller
Cylinder shell has the same content as one of its base. Cylinder height is 15 dm. What is the radius of the base of the cylinder?
20. 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°?

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