# Grade - examples - page 78

1. Theorem prove
We want to prove the sentence: If the natural number n is divisible by six, then n is divisible by three. From what assumption we started?
2. Fluid
We have vessels containing 7 liters, 5 liters and 2 liters. Largest container is filled with fluid the others empty. Can you only by pouring get 5 liters and two 1 liter of fluid? How many pouring is needed?
3. Cuboid - volume and areas
The cuboid has a volume of 250 cm3, a surface of 250 cm2 and one side 5 cm long. How do I calculate the remaining sides?
4. Barrel 2
Empty barrel weighs 7 kg. When it filled with water up to 45% height, weighs 60 kg. How heavy is barrel full of water?
5. Candies
In the box are 12 candies that look the same. Three of them are filled with nougat, five by nuts, four by cream. At least how many candies must Ivan choose to satisfy itself that the selection of two with the same filling? ?
6. Flywheel
Flywheel turns 450 rev/min (RPM). Determine the magnitude of the normal acceleration of the flywheel point which are at a distance of 10 cm from the rotation axis.
7. Brackets
Place one pair of brackets in expression 20-16 + 10 - 4 - 2 so that the result will be 0.
8. Tiles
How many 46 cm square tiles will cover a floor 22.08 m by 8.74 m?
9. Rectangle Anton
Difference between length and width of the rectangle is 8. Length is 3-times larger than the width. Calculate the dimensions of the rectangle.
10. Cross-sections of a cone
Cone with base radius 16 cm and height 11 cm divide by parallel planes to base into three bodies. The planes divide the height of the cone into three equal parts. Determine the volume ratio of the maximum and minimum of the resulting body.
11. Lion or virgin
We toss coin, every throw fits lion or a virgin with equal probability 1/2. Determine how much at least we have to make throws that with probability 0.9 lion fell at least once.
12. Apples and pears
Mom divided 24 apples and 15 pears to children. Each child received the same number of apples and pears - same number as his siblings. How many apples (j=?) and pears (h=?) received each child?
13. Round table tablecloth
Round table has area 50.24 dm2. Calculate the diameter of the circular tablecloth, if it is extend beyond the edge of the table by 30 cm.
14. Parcel
Both dimensions of the rectangular parcel were increased by 26%. By how many % has increased its acreage?
15. Every day 7 pages
Adelka reads the book every day 7 pages. When she reads one more page a day she will read it three days earlier. How long will Adelka read a book? How much does a book of pages have?
16. Tractor wheels
Smaller tractor wheel has a circumference of 3 meters, bigger 4 meters. On what path executes smaller wheel 6 turns over more bigger?
17. RT 10
Area of right triangle is 84 cm2 and one of its cathethus is a=10 cm. Calculate perimeter of the triangle ABC.
18. Silo
Outer perimeter of silo is 32 m. Concrete wall is 35 cm thick. What is diameter and area of inside floor of silo?
19. Water in aquarium
The aquarium cuboid shape with a length of 25 cm and a width of 30 cm is 9 liters of water. Calculate the areas which are wetted with water.
20. Motor oil
30 liters of oil cost 28.80 Euros. How much cost a liter?

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