# Examples for 8th grade - page 38

1. Rotary cylinder
The rotating cylinder has a surface area 69.08 cm2. The area of the shell is 62.8 cm 2. What is the diameter of the cylinder?
2. Painting rooms
If Dano paint three hours daily given work he complete in 7.5 days. How many hours a day would have to work to finish the job 1.5 days earlier?
3. The hall
The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m2. What were the original dimensions of the hall?
4. Diagonal in rectangle
In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts.
5. Homework - jumps
Sasha jumped 121 cm Peter 4 cm more than Jirka. Jirka 6 cm less than Misha. Misha 7 cm less than Filip and Filip half as much Sasha and Petr together. How far each jumped?
6. Eight blocks
Dana had the task to save the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be four
7. Tachometer
Tatra's tachometer shows the initial state 886123 km this morning. Tatra today travel at an average speed of 44 km/h. Determine the function that describes the Tatra's tachometer depending on the time. What is the state of tachometer after 4 hours?
8. Alloy
The first alloy is a mixture of two metals in the ratio 1:2, the second is a mixture of same metals in the ratio 2:3. At what ratio we have these two alloys put into the furnace to obtain a new metal alloy with ratio 17:27? (All three ratios correspond to.
Two fifth-graders teams competing in math competitions - in Mathematical Olympiad and Pytagoriade. Of the 33 students competed in at least one of the contest 22 students. Students who competed only in Pytagoriade was twice more than those who just competed
10. Two workers
Two workers make 138 parts/items. The first one produces 30% more than the second. How many items will each produce?
11. Arc
Convert to arc measures (radians): 924 ° Result write as a multiple of π
12. Workhorses
A team of colleagues done the work in 20 days. After adding 2 colleagues from the beginning the work was completed in 15 days. How many members has the colleague team?
13. Ratio
Unfold number 1963 in the ratio 9:2:2.
14. TV commercials
For the typical one-hour prime-time television slot, the number of minutes of commercials is 3/8 of the minutes of the actual program. Determine how many minutes of the program are shown in that one hour.
15. Hiker and cyclist
At 7 PM hiker started at 6 km/h to hike. After 3 hrs. later started on the same trip cyclist at speed of 15 km/h. After an hour of driving a flat tire and take him half hours to correct defect. At what time catch up cyclist with hiker?
16. Rope
How many meters of rope 10 mm thick will fit on the bobbin diameter of 200 mm and length 350 mm (central mandrel have a diameter 50 mm)?
17. Distance
Wha is the distance between the origin and the point (18; 22)?
18. Pot
Calculate the height of 3 liter pot with shape cylinder with a diameter of 10 cm.
19. Clocks
What distance will describe the tip of minute hand 6 cm long for 20 minutes when we know the starting position with finally enclose hands each other 120°?
20. Glass
Peter broke the window glass with size 110 cm and 90 cm. 1 square meter of glass costs 11 USD. How much money is need to pay for a new glass?

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