# Examples for 8th grade - page 45

1. Three digits number
From the numbers 1, 2, 3, 4, 5 create three-digit numbers that digits not repeat and number is divisible by 2. How many numbers are there?
2. Three friends
Three friends squirrels together went to collect hazelnuts. Zrzecka he found more than twice Pizizubka and Ouska even three times more than Pizizubka. On the way home they talked while eating and was cracking her nuts. Pizizubka eaten half of all nuts whi
3. 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.
5 km long road begins at an altitude 500 meters above sea level and ends at a altitude 521 ASL. How many permille road rises?
5. 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 ?
6. 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?
7. 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
8. Thales
Calculate the length of the Thales' circle described to right triangle with hypotenuse 18.4 cm.
9. Rectangle
The rectangle is 18 cm long and 10 cm wide. Determine the diameter of the circle circumscribed to rectangle.
10. Chord MN
Chord MN of circle has distance from the center circle S 120 cm. Angle MSN is 64°. Determine the radius of the circle.
11. The dice
What is the probability of events that if we throw a dice is rolled less than 6?
12. Clocks
How long track travel the second hand in 46 hours, the end of which is 4 cm long.
13. 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?
14. Deposit 3
After a year had Martin on bank account € 2028. What was the interest rate when the initial deposit was € 1879?
15. 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)
16. 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.
17. 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.
18. Triangle SSA
Construct a triangle ABC if |AB| = 5cm va = 3cm, CAB = 50 °. It is to create the analysis and construction steps.
19. Gravel - cone
Mound of gravel has shape of regular circular cone with a height 3.3 meter and a base circumference of 18.85 meters. How many cubic meters of gravel are in the pile? Calculate the weight of gravel if its density is p = 640 kg / cubic m.
20. 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.

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