Examples for 9th grade - page 14

  1. Circle section
    circle_segment Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector.
  2. 2x cone
    truncated_cone_2 Circular cone height 76 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone.
  3. 4s pyramid
    pyramid_regular Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height?
  4. Cut and cone
    kuzel Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
  5. Dice
    dices How many times must throw the dice, the probability of throwing at least one six was greater than 90%?
  6. Football league
    football In the 5th football league is 10 teams. How many ways can be filled first, second and third place?
  7. Jewel
    rhombus3 Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
  8. Triangular pyramid
    tetrahedron1 Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
  9. The chord
    Tetiva Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°?
  10. Trapezoid
    rectangular_trapezoid Are diagonals in a rectangular trapezoid perpendicular and bisect the angles?
  11. Square grid
    sit Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm2 and circumference 12 cm and that their sides is in square grid.
  12. Sequence
    arithmetic_seq In the arithmetic sequence is a1=-1, d=4. Which member is equal to the number 203?
  13. RT - hypotenuse and altitude
    pravy_trojuholnik Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments?
  14. Circle and angle
    arc What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad?
  15. Pillar
    sliced_pyramid Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48.
  16. Stock market
    money_1 Simon one day decided to invest € 62000 to the stock market. After six months he invested July 25 stock markets fell by 47%. Fortunately for Simon from July 25 5 to October 25 his shares have risen by 39%. Simon is then: ?
  17. Painter Pavel
    pixla_s_farbou Painter Pavel painted the fence for 16 hours and painter Petr the same fence painted for 13 h. How long should take painted the fence together?
  18. Discounts on rail (ZSSK)
    preukazy_zssk The railway company ZSSK offers a discount of 15% (REGIONAL) for 5 Eur/year. Calculate the real discount rate as a percentage, where passengers will travel 19 Eur per week.
  19. Balls
    balls_1 Ping pong balls have a diameter of approximately 4.6 cm. They are sold in boxes of 4 pieces: each box has the shape of a cuboid with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled w
  20. Accidents
    nehoda-pomnik The count of accidents in 1995 caused 8780 women which is 8.4%. How many men caused the accidents?

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