# Examples for 8th grade - page 65

1. Isosceles - isosceles It is given a triangle ABC with sides /AB/ = 3 cm /BC/ = 10 cm, and the angle ABC = 120°. Draw all points X such that true that BCX triangle is an isosceles and triangle ABX is isosceles with the base AB.
2. Cube Calculate the surface of the cube ABCDA'B'C'D' if the area of rectangle ACC'A' = 344 mm2.
3. Sines In ▵ ABC, if sin(α)=0.5 and sin(β)=0.6 calculate sin(γ)
4. Heating plant Workers dump imported coke at heating plant. On the first day used half of the amount, the second day three quarters the rest and on the third day left 120 tons. How much coke they dump at heating plant?
5. Three dice When you throw three dice was the sum total of the dice 10. The yellow dice fell one eye more than on the red and brown fell 3 eyes less than red. How many eyes fell on every dice?
6. Drainage channel The cross section of the drainage channel is an isosceles trapezoid whose bases have a length of 1.80 m, 0.90 m and arm has length 0.60 meters. Calculate the depth of the channel.
7. Book Alena read a book at speed 15 pages per day. If she read twice as fast she should read a book four days earlier. How many pages have a book?
8. Percentage and rectangle About what percentage increases perimeter and area of a rectangle if both the sides 12 cm and 10 cm long we increase by 20%?
9. Meat Half a kilogram of pork and three-quarters of a kilogram of beef cost total 5.1 USD. One quarter of a kilogram of beef and 1 kilogram of pork cost 4.9 USD. Determine the price of 1 kg of each type of meat.
10. Shoes and slippers Shoes were three times as many as slippers. If shoes were cheaper by 120, it would be twice as expensive as slippers. How much cost shoes and how much slippers?
11. Chord distance The circle k (S, 6 cm), calculate the chord distance from the center circle S when the length of the chord is t = 10 cm.
12. Saving The boy has saved 50 coins € 5 and € 2. He saved € 190. How many were € 5 and how many € 2?
13. Railway wagon The railway wagon holds 75 m3 load. Wagon can carry a maximum weight of 30 tonnes. What is the maximum density that may have material with which we could fill this whole wagon? b) what amount of peat (density 350 kg/m3) can carry 15 wagons?
14. Aquarium volume The aquarium has a cuboid shape and dimensions a = 0.3 m, b = 0.85 m, c =? , V = ?. What volume has a body, if after dipping into the aquarium water level rises by 28 mm?
15. Trapezoid v3 The isosceles trapezoid has the angle at a firsst base 40 degrees less than the angle at second base. How large angles has this trapezoid ?
16. Diamond Calculate the length of the two diagonals of the diamond if: a = 13 cm v = 12 cm
17. Mortgage Family XY wants to take the bank mortgage (loan for an apartment/house) in the amount of € 100,000. Bank for processing the mortgage charges a fee of 0.79% of the amount borrowed. How many euros is this fee?
18. Coins In ticket maschine were together one hundred coins. They were only 20 and 50 cent coins. The sum total was 29 euros and 60 cents. How many were in ticket maschine coins and which type?
19. Rain How many mm of water rained the roof space 75 m2 if the empty barrel with a radius of 8 dm and height 1.2 m filled to 75% its capacity? :-)
20. Cone area and side Calculate the surface area and volume of a rotating cone with a height of 1.25 dm and 17,8dm side.

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