# Algebra - problems - page 14

1. Spherical segment
Spherical segment with height h=6 has a volume V=134. Calculate the radius of the sphere of which is cut this segment.
2. Divisibility
Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16.
3. Pumps
Pump that draws water at velocity 3.5 liters per second water from a construction trench take 35 minutes. a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second. b) What is the pumping velocity wo
4. Sphere and cone
Within the sphere of radius G = 36 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone?
5. AVG of INT
What is the average of the integers from 9 throuht 52 inclusive?
6. Circle
From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
7. Fractions
Sort fractions ? by its size. Result write as three serial numbers 1,2,3.
8. Lines
Five bus lines runs at intervals 3, 6, 9, 12, 15 minutes. In the morning, suddenly start at 4:00. After how many minutes the bus lines meet again?
9. Tractors
Six tractors plowing the field for 8 days. After two days, two tractors broke down. How many days were prolonged work in the field?
10. Working time - shortening
The media often speculates about the change (especially to shorten) the working time of the five-day eight-hour working week to another working model. Calculate how many hours a day the employee would have to work a day at 3-day work week if he must work t
11. Fertilizer
Mr. Gherkin use for fertilization 8% solution of fertilizer. 4 liters of it still left. How much water must be added to the solution to make only 4% solution?
12. Circular sector
I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector?
13. Pizza master
Master says that he can splits pizza to 16 parts by five equals straight cuts. Is it possible?
14. Denominator
Calculate the missing denominator x: ?
15. Purchase
Mother bought 5 boxes of milk and 7 kg of potatoes and paid a total CZK 147. Aunt bought 7 boxes of milk and 3 kg of potatoes and paid 131 CZK. What is the price of one carton of milk and 1 kg of potatoes? How CZK together would have saved if bought at the
16. Pedestrian and cyclist
Pedestrian out with a speed of 4 km/hour from city center and after 1hour and 10 minutes came after him cyclist at speed of 18 km/h. At how many minutes he catches up with pedestrian?
17. Cinema
Cinema auditorium is built for 3300 people. The first row is planned for 36 seats and each next gradually 4 more. How many rows of seats will have auditorium?
18. Hiker
Hiker went half of trip the first day, the third of trip the second day and remaines 15 km. How long trip he planned?
19. Tiles
Hall has dimensions 325 &time; 170 dm. What is the largest size of square tiles that can be entire hall tiled and how many we need them?
20. Car factory
Carmaker now produce 4 cars a day more than last year, so the production of 388128 cars will save just one full working day. How many working days needed to manufacture 388128 cars last year?

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