# Examples for 7th grade (seventh) - page 29

1. Water pool
Pool with volume 990hl completely filled, if water flows by one tap 8 hours and by second tap 6 hours. First tap give 10hl more than second per hour. How many hl flows in each of them in an hour?
2. Triangle
For how many integer values of x can 16, 15 and x be the lengths of the sides of triangle?
3. Diameter
What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm?
4. Canister
Gasoline is stored in a cuboid canister having dimensions 44.5 cm, 30 cm, 16 cm. What is the total weight of a full canister when one cubic meter of gasoline weighs 710 kg and the weight of empty canister is 1.5 kg?
5. Slope RR
A line has a rise of 2 and a run of 11. What is the slope?
6. Cuboid - simple
Calculate the surface area and volume of a cuboid if a = 8 cm, b = 14 cm and c = 6 cm.
7. Midpoint of segment
Point A has coordinates [-16; 23] and the midpoint of the segment AB is the point [2; 12]. What are the coordinates of point B?
8. Tippler
Bottle with cork cost 8.8 Eur. The bottle is 0.8 euros more expensive than cork. How much is a bottle and the cork?
Car started at 11:40 at speed 54 km/h from A and to B arrived at 12:20. Determine the distance A and B.
10. Lie/do not lie
The function is given by the rule f(x) = 8x+16. Determine whether point D[-1; 8] lies on this function. Solve graphically or numerically and give reasons for the your answer.
11. Decomposition
Make decomposition using prime numbers of number 155. Result write as prime factors (all, even multiple)
In the square ABCD point P is in the middle of the DC side and point Q in the middle pages AD. If the area of quadrilateral BQPC is 49 cm2, what is the area of ABCD?
13. Right triangle
Right triangle ABC with side a = 19 and the area S = 95. Calculate the length of the remaining sides.
Once upon a time, we learned in school that the Russians have "wider" tracks than our, because they have less tolerable ground. In truth, decide olny area of sleepers, no track gauge. Calculate how many millimeters, our track 1435 mm different from the R
15. Rabbits
Michael breeding rabbits. His 7 rabbits will eat 98 feed rations for 7 days. How many equal portions of feed should be eat 5 rabbits in 6 days?
16. Tons of coal
Coal hopper has a capacity of 285 liters. How many tons is it? The bulk density of coal is 916 kg/m3.
17. Czech crowns
Small Petra save money. Grandfather give her 10 crowns. Petra asked his older sister let her calculate how much he has saved up. Sister told her that he has less than 30 crowns. If the sum is divided by three left one crown. If the sum is divided by the f
18. Average
Average of 7 numbers is 65. What is its sum?
19. Office rent
For rent 1m2 of office space is paid €165 per year. How much is the annual rent for an office as big as a football field with dimensions 71.5 m and 102.5 m?