Examples for 9th grade - page 4

  1. Cubes
    squares_2 One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
  2. Discount
    pulover Ladies sweater was twice discounted. First by 11%, then by 11% of the new price. Its final price was 100 €. Determine the original price of sweater.
  3. Transforming cuboid
    cube Cuboid with dimensions 6 cm, 10, and 11 cm is converted into a cube with the same volume. What is its edge length?
  4. 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.
  5. Rhombus
    rhombus Calculate the perimeter and area of ​​a rhombus whose diagonals are 38 cm and 55 cm long.
  6. Short cut
    direct_route Imagine that you are going to the friend. That path has a length 330 meters. Then turn left and go another 2000 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?
  7. Gimli Glider
    gimli_glider Aircraft Boeing 767 lose both engines at 42000 feet. The plane captain maintain optimum gliding conditions. Every minute, lose 1910 feet and maintain constant speed 211 knots. Calculate how long it takes to plane from engine failure to hit the ground. Ca
  8. River
    river From the observatory 11 m high and 24 m from the river bank, river width appears in the visual angle φ = 13°. Calculate width of the river.
  9. 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?
  10. Cube diagonal
    cube_diagonal Determine the length of the cube diagonal with edge 75 mm.
  11. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 7 cm.
  12. Logs
    gulatina Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
  13. Sphere
    1sphere The surface of the sphere is 12100 cm2, and weight is 136 kg. What is its density?
  14. Right triangle Alef
    r_triangle The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
  15. Rectangle
    diagonal In rectangle with sides, 6 and 3 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?
  16. No. of divisors
    triangle_div How many different divisors have number ??
  17. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  18. 7 heroes
    7statocnych 9 heroes galloping on 9 horses behind. How many ways can sort them behind?
  19. Vinegar 2
    ocet How many percentage of getvinegar solution, if we mix to 3.5 liters of 5.8% and 5 liters of 7.6% vinegar?
  20. Rhombus ABCD
    rhombus6 Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.

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