# Examples for 9th grade - page 15

1. Trapezoid - diagonal Trapezoid has a length of diagonal AC corssed with diagonal BD in the ratio 2:1. The triangle created by points A, cross point of diagonals S and point D has area 164 cm2. What is the area of the trapezoid?
2. House roof The roof of the house has the shape of a regular quadrangular pyramid with a base edge 17 m. How many m2 is needed to cover roof if roof pitch is 57° and we calculate 11% of waste, connections and overlapping of area roof?
3. V-belt Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
4. Wire D Wire length 1 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle.
5. Triangle in circle Vertices of the triangle ABC lies on a circle with radius 3 so that it is divided into three parts in the ratio 4:4:4. Calculate the circumference of the triangle ABC.
6. Cyclists Cyclist who rides at an average speed 16 km/h travels trip distance 10 min before the cyclist who rides at an average speed 11 km/h. What is the length of this cyclist trip(distance in km)?
7. Sphere A2V Surface of the sphere is 241 mm2. What is its volume?
8. Two balls Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.
9. Hollow sphere Steel hollow sphere floats on the water plunged into half its volume. Determine the outer radius of the sphere and wall thickness, if you know that the weight of the sphere is 0.5 kg and density of steel is 7850 kg/m3
10. Cardboard box We want to make a cardboard box shaped quadrangular prism with rhombic base. Rhombus has a side of 5 cm and 8 cm one diagonal long. The height of the box to be 12 cm. The box will be open at the top. How many square centimeters cardboard we need, if we cal
11. Trigonometry If you know that cos(γ) = sin (806°), what is the angle γ?
12. Magnification of the square If we increase the square side, increase the content of the 80 %. About what percentage was increased his sides?
13. Arm Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 18 cm and a height v=17 cm.
14. Scouts The boys from scout group traveled 5 days distance 115 km. Every day walked 1.5 km less than the previous day. How many kilometers scouts walked in the first day?
15. Morse alphabet Calculate how many words of Morse code to create compiling commas and dots in the words of one to four characters.
16. Tanker An oil tanker can be emptied by the first pump in 4.9 hours. Second pump can empty an tanker in 8 hours. If the first pump started at 4:00 and second 1.4 hour later, at what time will the tanker be empty?
17. Cone and the ratio Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
18. Q-Exam If tg α = 0.9, Calculating sin α, cos α, cotg α .
19. Triangle angles The angles α, β, γ in triangle ABC are in the ratio 6:2:6. Calculate size of angles.
20. Sector The perimeter of a circular sector with an angle 1.8 rad is 64 cm. Determine the radius of the circle from which the sector comes.

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