# Problems for 7th grade (seventh)

1. Winch
The steel rope has a diameter of 6mm and a length of 20m. We are winding on drum width 60mm, starting diameter 50mm. What is the final diameter after winding?
2. Delayed clock
Michael put a new battery into his watch at midnight. However, they are 5 seconds late each minute. How many hours does the watch show in 24 hours?
3. Iceberg
What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg?
4. Tourist
A tourist walked an average speed of 3.5 km/h route in 6 hours. Calculate how many hours he would have passed at an average speed of 5.5 km/h.
5. Geometric plan
At what scale the building plan if one side of the building is 45m long and 12mm long on a plan?
6. Down syndrome
Down syndrome is one of the serious diseases caused by a gene mutation. Down syndrome occurs in approximately every 550-born child. Express the incidence of Down's syndrome in newborns at per mille.
7. Cube into cylinder
If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
8. Iron pole
The iron pole is in the ground 2/5 of its length, partly above the ground 1/3 is yellow, and the unpainted section is 6 m long. How long is the entire column?
9. Cook on gas
The gas cylinder will last for 30 weekends for 2 hours of daily cooking. How many days will we be able to cook on a new cylinder when we cook 3 hours a day?
10. Dance group
The dance group formed groups of 4, 5, and 6 members. Always one dancer remains. How many dancers were there in the whole group?
11. Barter
There is exchange trade on the market. We know that for two sheepskins we get three goat skins. We also know that for six rabbits skins we get four goat skins. How many rabbit's skins we get for four sheepskins?
12. Temperature change
The mean temperature change is -3.2°F per day for five days. What is the total change over the five day period?
13. Last page
Two consecutive sheets dropped out of the book. The sum of the numbers on the sides of the dropped sheets is 154. What is the number of the last page of the dropped sheets?
14. Prism 4 sides
Find the surface area and volume four-sided prism high 10cm if its base is a rectangle measuring 8 cm and 1.2dm
15. The King
The King wants to divide his sons equally. He has 42 rubies and 45 diamonds. How many sons and how will they share them?
16. Four workers
Four workers will lay the floor of the gym in six hours. After an hour of working together, one of the workers left to the doctor. How long before the remaining three workers finish their work?
17. Area of rectangle
How many times will increase the area of the rectangle, if we increase twice the length and at the same time we decrease the width by the half?
18. MG=7x-15,
MG=7x-15, FG=33, x=? Point M is the midpoint of FG. Find unknown x.
19. Midpoint 6
FM=8a+1, FG=42, a=? Point M is the midpoint of FG. Find unknown a.
20. Midpoint 5
FM=3x-4, MG=5x-26, FG=? Point M is the midpoint of FG. Use the given information to find the missing measure or value.

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