Examples for 8th grade - page 4

  1. Short cut
    direct_route Imagine that you are going to the friend. That path has a length 330 meters. Then turn doprava and go another 840 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?
  2. 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.
  3. Discount
    pulover Ladies sweater was twice discounted. First by 17%, then by 17% of the new price. Its final price was 72 USD. Determine the original price of sweater.
  4. 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 137 cm2.
  5. Regular 5-gon
    5gon_2 Calculate area of the regular pentagon with side 11 cm.
  6. Rhombus
    rhombus Calculate the perimeter and area of ​​rhombus whose diagonals are 15 cm and 27 cm long.
  7. Logs
    gulatina Trunk diameter is 79 cm. Is it possible to inscribe a square prism with side 75 cm?
  8. Right triangle Alef
    r_triangle The perimeter of a right triangle is 132 cm, the hypotenuse is 55 cm long. Determine the lengths of the legs.
  9. Motion2
    car_cycle Cyclist started out of town at 20 km/h. After 0.6 hours car started behind him in the same direction and caught up with him for 52 minutes. How fast and how long went car from the city to caught cyclist?
  10. Sphere
    1sphere Surface of the sphere is 2260 cm2, weight is 52.2 kg. What is its density?
  11. Square and circles
    kruznica_stvorec_1 Square with sides 89 m is circumscribed and inscribed with circles. Determine the radiuses of both circles.
  12. ŽSR
    luzianky Calculate fixed annual personnel costs of operating monorail line 106 km long if every 5 km is station, which serve three people - one dispatcher and two switchman in 3-shift operation. Consider the average salary of the employee 847 €.
  13. Proof PT
    pytagoras Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
  14. Rectangle
    diagonal In rectangle with sides 10 and 9 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?
  15. Rhombus ABCD
    rhombus6 Rhombus ABCD, |AC| = 42 cm, |BD| = 96 cm. Calculate the perimeter of the rhombus ABCD.
  16. Diagonal
    rectangle_diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 6 cm, b = 7 cm.
  17. No. of divisors
    triangle_div How many different divisors has number ??
  18. Two cars
    cars_racing Two cars started against each other at the same time to journey long 225 km. First car went 35 km/h and second 48 km/h. What distance will be between this cars 20 minutes before meet?
  19. Area of RT
    right_triangle_sepia Calculate the area of a right triangle which hypotenuse has length 20 and one hypotenuse segment has lenght 15.
  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 4.8 kg?

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