# Examples for 8th grade - page 60

1. Outer angles The outer angle of the triangle ABC at the A vertex is 71°40 ' outer angle at the vertx B is 136°50'. What size has the inner triangle angle at the vertex C?
2. Salt 1 t of sea water contains 25 kg of salt. How many tons of seawater must be evaporated to obtain 2 q of salt? On a weekly forest brigade operates 12 students. After plant one hundred spruces get x CZK, anfter one hundred pines y CZK. How many CZK got one student for one day if planted spruces 25000 and 30000 pines week?
4. Translations If I going to translate the book 6 pages per day I translate it 4 days earlier than if I translated 5 pages a day. If I translate 4 pages a day I translate it for how many days.....?
5. Painters 15 painters painted fence for 280 minutes. For how many minutes paint half of this fence 12 painters?
6. Mason with assistant Mason had to complete the work in 10 days. Two and a half days later his assistant arrived. Together they completed the work in next three and a half days. How many days would he need an assistant for the same work?
7. Work at plant Handyman has vowed to do repair work at the plant for 25 days. However, work had to be shortened and therefore gained helper. Together they made all the corrections for 13 1/3 days. How long the work would take helper himself?
8. Well Rope with a bucket is fixed on the shaft with the wheel. The shaft has a diameter 50 cm. How many meters will drop bucket when the wheels turn 15 times?
9. Four classses Students of all 7, 8 and 9 classes in one school may take up 4,5,6 and 7 abreast and nobody will left. How many is the average count of pupils in one class if there are always four classes each grade?
10. Sisters Sisters Janka and Danka are saved together 220 CZK. On a trip to Janka wants to take a fifth of her savings and Danka quarter. Then they will have 50 CZK on the trip. How much money saved Janka and Danka?
11. Percentage reduction Reducing the unknown number by 19% get number 700.7 Determine unknown number.
12. Trapezium The length of the base and the height size of the base of the trapezium is at ratio 5:3:2, the content area of the trapezium is 128 cm2. Calculate the length of the base and the height of the trapezoid.
13. Diagonals Draw a square ABCD whose diagonals have a length of 6 cm
14. Triangular prism Calculate the volume and surface of the triangular prism ABCDEF with base of a isosceles triangle. Base's height is 16 cm, leg 10 cm, base height vc = 6 cm. The prism height is 9 cm.
15. Isosceles trapezoid In an isosceles trapezoid KLMN intersection of the diagonals is marked by the letter S. Calculate the area of trapezoid if /KS/: /SM/ = 2:1 and a triangle KSN is 14 cm2.
16. Resort In a completely crowded resort was 30% from the Czech Republic quarter visitors were from Slovakia and the rest 135 came from Germany. What capacity have resort?
17. Plan scale At what scale is drawn plan of the building, where one side of the building is 45 meters long is on the plan expressed by a straight line 12 mm long.
18. Is right? Determine whether the triangle with legs (catheti) 19.5 cm and 26 cm and length of the hypotenuse 32.5 cm is rectangular?
19. Triangle midpoints Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC.
20. Prism Calculate the height of the prism having a surface area 448.88 dm² wherein the base is square with a side of 6.2 dm. What will be its volume in hectoliters?

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