# Examples for 7th grade (seventh) - page 30

1. Rectangle and circle
The rectangle ABCD has side lengths a = 40 mm and b = 30 mm and is circumscribed by a circle k. Calculate approximately how many cm is circle long.
2. Trees
Loggers wanted to seed more than 700 and less than 800 trees. If they seed in rows of 37, left them 8 trees. If they seed in rows of 43, left the 11 trees. How many trees must seed ?
3. Machines 2
2 machines for 50 hours produces 2,000 products. How many machines need to buy to make in 30 hours 15,000 products?
4. Oil tank and pipes
The underground oil tank can be filled by two oil pipelines. The first is filled in 72 hours and the second in 48 hours. How many hours from the moment when first pipeline began to fill the oil is it necessary to start filling it with the second to fill in
5. Octagon from rectangle
From tablecloth rectangular shape with dimensions of 4 dm and 8 dm we cuts down the corners in the shape of isosceles triangles. It thus formed an octagon with area 26 dm2. How many dm2 we cuts down?
6. Chicken and rabbits (classic)
Grandmother breeding chickens and rabbits. It found that the yard has 35 heads and 108 legs. How many chickens and rabbits breeding in the yard?
7. Water in body
Water in the human organism of all the compounds represented, constitutes about 3/5 of the total weight. How many kilograms of water is in your body when you weigh 67 kg?
8. Total displacement
Calculate total displacement of the 4-cylinder engine with the diameter of the piston bore B = 6.6 cm and stroke S=2.4 cm of the piston. Help: the crankshaft makes one revolution while the piston moves from the top of the cylinder to the bottom and back.
9. Clocks
How long track travel the second hand in 46 hours, the end of which is 4 cm long.
10. Tractors
6 tractors started plowing the field that them together take 12 days. Agronomist hesitates to A) after 2 days to withdraw 2 tractors, or B) after 3 days to withdraw 3 tractors. Help him which of these two cases will be plowing done sooner.
11. Deposit 3
After a year had Martin on bank account € 2028. What was the interest rate when the initial deposit was € 1879?
12. Bakery
How heavy must prepare bread at a bakery if lose during baking 16% of water and after baking must have 2 kg? (Calculate to the nearest gram)
13. Two pumps
The first pump fills the tank in 24 hours second pump in another 40 hours. For how long will take fill the tank if operate both pumps at the same time?
14. Olympics
In how many ways can be placed 6 athletes on the podium at the Olympics? Depend on the color of the metal.
15. Circular flowerbed
Circular flowerbed with diameter 8 m we split by concentric circle to circle and annulus with the same area. Determine the radius of the circle.
16. Dig water well
Mr. Zeman digging a well. Its diameter is 120 cm, and plans to 3.5 meters deep. How long (at least) must be a ladder, after which Mr. Zeman would have eventually come out?
17. Bottle
Bottle with wine costs 58 USD. Wine is 27 USD more expensive than the empty bottle. How much is the bottle itself?
18. Beer permille
In the 5 kg of blood of adult human after three 10° beers consumed shortly after another is 6.6 g of the alcohol. How much is it as per mille?
19. Clock
How long is trajectory of second hand of hours for day, if is 15 mm long?
20. Wheel
How many times turns the wheel of a passenger car in one second if car run at speed 100 km/h. Wheel diameter is d = 62 cm.

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