Grade - examples - page 31

  1. Hexagonal prism
    hexa_prism The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
  2. Divisibility
    dots Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16.
  3. Minute angle
    watch Determine size of angle, which takes minute hand for 75 minutes.
  4. Shooter
    terc_1 The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?
  5. Cube
    cube2 The sum of lengths of cube edges is 69 cm. What is its surface and volume?
  6. Wiring
    install_pipes Conduit has a cross section 482 mm. Maybe put it into 6 conductors with a cross section S2 $mm2?
  7. Mystery of stereometrie
    Tetrahedron Two regular tetrahedrons have surfaces 88 cm2 and 198 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
  8. Nine-gon
    9gon_1 Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
  9. Pumps
    water_pump Pump that draws water at velocity 3.5 liters per second water from a construction trench take 35 minutes. a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second. b) What is the pumping velocity wo
  10. Compass
    wind_rose What angle are between directions WSW (WestSouthWest) and SSE (SouthSouthEast) on the compass?
  11. Sphere and cone
    cone_in_sphere Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
  12. 3y inflation
    bread Price of the roll rise in the first year by 9%, the second year fell by 5% and in the third year increased by 3%. Calculate the average annual increase in price of the roll.
  13. Lock
    combination-lock Combination lock will open when the right choice of 5 numbers (from 1 to 12 inclusive) is selected. A. How many different lock combinations are possible? B. Is he combination lock named appropriately?
  14. Side c
    trig-cos-law In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
  15. Pit
    truncated_pyramid Pit has shape of a truncated pyramid with rectangular bases and is 0.8 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.6 l of green colour. How many liters of paint is needed when w
  16. Ratio
    pomer Increase in the ratio 20:4 number 18.5.
  17. Black building
    talapka_cierna_stavba Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchin
  18. Road
    route-66 Average climb of the road is given by ratio 1:15. By what angle road average climb?
  19. Height difference
    road What height difference overcome if we pass road 1 km long with a pitch21 per mille?
  20. Circle
    circles From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.

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