Examples for 9th grade - page 16

  1. V-belt
    v_belt Calculate the length of the belt on pulleys with diameters of 105 mm and 393 mm at shaft distance 697 mm.
  2. Wire D
    semicircle_1 Wire length 1 m is bent so that it forms a semicircle circuit (including the diameter). Determine the radius of the semicircle.
  3. Triangle in circle
    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.
  4. Cyclists
    cyclist_3 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)?
  5. Sphere A2V
    sphere3 Surface of the sphere is 241 mm2. What is its volume?
  6. Two balls
    balls-inside-cylinder 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.
  7. Hollow sphere
    sphere_2 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
  8. Cardboard box
    krabicka 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
  9. Trigonometry
    trigonometry If you know that cos(γ) = sin (806°), what is the angle γ?
  10. Magnification of the square
    square If we increase the square side, increase the content of the 80 %. About what percentage was increased his sides?
  11. Arm
    arm Calculate the length of the arm r of isosceles triangle ABC, with base |AB| = 14 cm and a height v=18 cm.
  12. Scouts
    skauti_1 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?
  13. Morse alphabet
    morse_code Calculate how many words of Morse code to create compiling commas and dots in the words of one to four characters.
  14. Tanker
    oil-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?
  15. Cone and the ratio
    kuzel 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.
  16. Q-Exam
    unit_circle If tg α = 0.9, Calculating sin α, cos α, cotg α .
  17. Triangle angles
    triangles_2 The angles α, β, γ in triangle ABC are in the ratio 6:2:6. Calculate size of angles.
  18. Sector
    vysec 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.
  19. EQL triangle
    rs_triangle Calculate inradius and circumradius of equilateral triangle with side a=77 cm.
  20. Amazing number
    numbers4 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.

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