# Examples for 9th grade - page 96

1. A cylinder A cylinder 108 cm high has a circumference of 24 cm. A string makes exactly 6 complete turns around the cylinder while its two ends touch the cylinder's top and bottom. (forming a spiral around the cylinder). How long is the string in cm?
2. Four painters The company sent four painters to paint the school. They should be done in 12 days. After three days, one painter got ill. How long will the remaining painters paint the school?
3. Final exam There are 5 learners in a class that has written a final exam Aleta scored 55% vera scored 36% and Sibusiso scored 88% if Thoko scored 71% and the class average was 63%. What was Davids score as a percentage?
4. Flowers 2 Cha cruz has a garden. The ratio roses to tulips is 2 : 5, the ratio of roses to orchids is 7 : 6. Cha cruz wonders what the ratio of tulips to orchids is. If Cha cruz has 183 plants, how many of each kind are there?
5. In the orchard In the orchard, they planted 25 apple trees, 20 pears, 15 plums and 40 marbles. A strong late frost, however, destroyed a fifth of all new trees. Unfortunately, it was all the trees of one kind of fruit. What is the probability that the plums have died out
6. Peaches There are 20 peaches in the pocket. 3 peaches are rotten. What is the probability that one of the randomly picked two peaches will be just one rotten? The double ladder is 8.5m long. It is built so that its lower ends are 3.5 meters apart. How high does the upper end of the ladder reach?
8. Tractors Wheel and belt tractors each day plow 8 ha of fields. For plow 76 hectares, the wheel would have to work for 12 days and 8 days with the belt tractor together. How many hectares do each day of each tractor?
9. Lathe 95% of the components manufactured on the lathe comply with the standard, of which 80% of the components are first-class. How likely can we expect a manufactured part to be first class?
10. Isosceles trapezium Calculate the area of an isosceles trapezium ABCD if a = 10cm, b = 5cm, c = 4cm.
11. Hectoliters How many hectoliters of water is in garden barrel with 90 cm diameter and a height of 1.3 m, if it is filled to 80% of its capacity?
12. Subsets How many 19 element's subsets can be made from the 26 element set?
13. Cube cut In the ABCDA'B'C'D'cube, it is guided by the edge of the CC' a plane witch dividing the cube into two perpendicular four-sided and triangular prisms, whose volumes are 3:2. Determine in which ratio the edge AB is divided by this plane.
14. Tv screen The size of a tv screen is given by the length of its diagonal. If the dimension of a tv screen is 16 inches by 14 inches, what is the size of the tv screen?
15. Boys to girls The ratio of boys to girls in a party is 3:5 . If 6 more boys arrived and 4 girls left the party, the ratio of boys to girls would be 5:6 . How many are in the party originally?
16. Two airports Two airports are 2690 km away. From the first airport, the airplane flies at a speed of 600 km/h, from a second airplane at a speed of 780 km/h. When will they meet if they flew at 10:00? How far from the first airport? What overload in g (g-force) has passed the pilot if he accelerated from 0 to 600 km/h in 3 seconds?
18. Red diplomas He numbers of students with honors in 2013 and 2014 are in ratio 40:49. How big is the year-on-year percentage increase?
19. Pupils There are 350 girls in the school, and the other 30% of the total number of pupils are boys. How many pupils does the school have?
20. Mixing water The 30-liter container should we fill with water at 60 degrees Celsius. How many liters of water 80 degrees C hot and how many liters of water 20 degrees Celsius warm we have to mix?

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