Examples for 9th grade - page 72

  1. Land - isosceles trapezoid
    lichobeznik-stredni_pricka_1 Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
  2. Three numbers
    trojuhelnikova_cisla What is three numbers which have the property: the sum of the reciprocals of the first and second numbers is 12/7, the first and third 11/24 and the second and the third 3/8.
  3. Tickets
    stadion_1 On the football tournament ticket cost 45 Kc for standing and 120kč for sitting. Sitting spectators was 1/3 more than standing. The organizers collected a total 12 300 Kc. How many seated and standing seats (spectators)?
  4. Roof 8
    veza_1 How many liters of air are under the roof of tower which has the shape of a regular six-sided pyramid with a 3,6-meter-long bottom edge and a 2,5-meter height? Calculate the supporting columns occupy about 7% of the volume under the roof.
  5. Church roof 2
    skleneny-kuzel The roof has the shape of a rotating cone shell with a base diameter of 6 m and a height of 2.5 m. How many monez (CZK) will cost the roof cover sheet if 1 m2 of metal sheet costs 152 CZK and if you need 15% extra for joints, overlays and waste?
  6. Two numbers
    maxwells-equation We have two numbers. Their sum is 140. One-fifth of the first number is equal to half the second number. Determine those unknown numbers.
  7. Chord circle
    Tetiva_1 The circle to the (S, r = 8 cm) are different points A, B connected segment /AB/ = 12 cm. AB mark the middle of S'. Calculate |SS'|. Make the sketch.
  8. Brick wall
    plot_zed Garden 70 m long and 48 m wide should surround with wall 2.1 meters high and 30 cm thick. Wall will be built on the garden ground. How many will we need bricks if to 1 m³ is required approximately 300 bricks?
  9. Three-digit
    seven How many three-digit natural numbers do not have the number 7?
  10. Divisible by 5
    175px-5th_MarDiv How many three-digit odd numbers divisible by 5, which are in place ten's number 3?
  11. Cuboid enlargement
    cubes_12 By how many percent increases the volume of cuboid if its every dimension increases by 30%?
  12. Bags
    kufor The first bag has a weight of 18 kg, the second bag is a one-third lighter than the first and the third bag has three times less the weight of all three bags together. Determine their weights.
  13. Angles in ratio
    angles_1 The size of the angles of the triangle are in ratio x: y = 7: 5 and the angle z is 42° lower than the angle y. Find size of the angles x, y, z.
  14. Water reservoir
    vodojem The reservoir shape of a cylinder having a diameter 8 m and a height 2.8 m. The device indicates that the reservoir contains 800 hectoliters of water. Calculate how much % of volume is used.
  15. AP 6
    progression_ao Calculate the first five items of an arithmetic sequence if it is given: a2 – a3 + a5 = 20 a1 + a6 = 38
  16. Tree shadow 3
    tree3_1 A 2-meter rod casts a shadow 3.2 m long. How high is a tree with a shadow of 14.4 m ?
  17. Body diagonal
    cubes3_1 Find the cube surface if its body diagonal has a size of 6 cm.
  18. Balls
    spheres_1 The urn is 8 white and 6 black balls. We pull 4 randomly balls. What is the probability that among them will be two white?
  19. Four friends
    money_10 Four friends shared the money. Vasek got 1/4 of the total amount. Tonda received 1/3 of the rest of the money, Joe got a half from the second residue and Jirka left 80. How much money get together?
  20. Axial cut
    Kuzel The cone surface is 388.84 cm2, the axial cut is an equilateral triangle. Find the cone volume.

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