Examples for 9th grade - page 5

  1. Cone A2V
    popcorn Surface of cone in the plane is a circular arc with central angle of 126° and area 415 cm2. Calculate the volume of a cone.
  2. Short cut
    direct_route Imagine that you are going to the friend. That path has a length 270 meters. Then turn left and go another 1810 meters and you are at a friend's. The question is how much the journey will be shorter if you go direct across the field?
  3. Transforming cuboid
    cube Cuboid with dimensions 8 cm, 13 and 16 cm is converted into a cube with the same volume. What is its edge length?
  4. Gimli Glider
    gimli_glider Aircraft Boeing 767 lose both engines at 44000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 2000 feet and maintain constant speed 196 knots. Calculate how long takes to plane from engines failure to hit ground. Calculate
  5. Rhombus
    rhombus Calculate the perimeter and area of ​​rhombus whose diagonals are 38 cm and 55 cm long.
  6. Scale
    pool_1 Swimming pool is long 110 m and 30 m wide. The plan of the city is shown as a rectangle with area 8.25 cm2. What scale is the city plan?
  7. River
    river From the observatory 14 m high and 32 m from the river bank, river width appears in the visual angle φ = 20°. Calculate width of the river.
  8. Cube diagonal
    cube_diagonal Determine length of the cube diagonal with edge 75 mm.
  9. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 7 cm.
  10. Logs
    gulatina Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
  11. Right triangle Alef
    r_triangle The area of a right triangle is 294 cm2, the hypotenuse is 35 cm long. Determine the lengths of the legs.
  12. Sphere
    1sphere Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
  13. Rectangle
    diagonal In rectangle with sides 3 and 10 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
  14. No. of divisors
    triangle_div How many different divisors has number ??
  15. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  16. 7 heroes
    7statocnych 9 heroes galloping on 9 horses behind. How many ways can sort them behind?
  17. Rhombus ABCD
    rhombus6 Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
  18. Diagonal
    rectangle_diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
  19. Vinegar 2
    ocet How many percentage of getvinegar solution, if we mix to 2 liters of 5.9% and 2 liters of 3.5% vinegar?
  20. Eiffel Tower
    eiffel_tower Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made ​​of the same material, if it weigh is 2.4 kg?

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