# Examples for secondary school students - page 13

1. 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
2. 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
3. Trigonometry If you know that cos(γ) = sin (806°), what is the angle γ?
4. Box Cardboard box shaped quadrangular prism with a rhombic base. Rhombus has a side 5 cm and one diagonal 8 cm long and height of the box is 12 cm. The box will open at the top. How many cm2 of cardboard we need to cover overlap and joints that are 5% of ar
5. 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?
6. Morse alphabet Calculate how many words of Morse code to create compiling commas and dots in the words of one to four characters.
7. Train The train is running at speeds of 96 km/h. From the beginning of braking to full stop train run for 3.3 minutes. If the train slows the braking equally, calculate the distance of the place from the station where you need to start to brake.
8. Q-Exam If tg α = 0.9, Calculating sin α, cos α, cotg α .
9. 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.
10. EQL triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
11. Amazing number An amazing number is name for such even number, the decomposition product of prime numbers has exactly three not necessarily different factors and the sum of all its divisors is equal to twice that number. Find all amazing numbers.
12. Block Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
13. Vector Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
14. Euklid4 Legs of a right triangle have dimensions 244 m and 246 m. Calculate the length of the hypotenuse and the height of this right triangle.
15. Geodesist Triangle shaped field (triangle ABC) has side AB = 129 m. path XY is parallel to the side AB which divided triangle ABC into two parts with same area. What will be the length of the path XY? Help please geodesist ...
16. Spherical segment Spherical segment with height h=6 has a volume V=134. Calculate the radius of the sphere of which is cut this segment.
17. XY triangle Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
18. Heron backlaw Calculate missing side in a triangle with sides 17 and 34 and area 275.
19. Coin and die Flip a coin and then roll a six-sided die. How many possible combinations are there?
20. Slope of the pool Calculate slope (rise:run) of the bottom of swimming pool long 30 m. Water depth at beginning of pool is 1.13 m (for children) and depth at end is 1.84 m (for swimmers). Slope express as percentage and as angle in degrees.

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