# Examples for 9th grade - page 17

1. Block
Calculate the volume of a cuboid ABCDEFGH if |AB| = 16 cm, |BC| = 19 cm and the angle ∠CDG = 36.9°
2. Amazing number
An amazing number is name for such even number, the decomposition product of prime numbers has exactly three not necessarily different factors and the sum of all its divisors is equal to twice that number. Find all amazing numbers.
3. Vector
Calculate length of the vector v⃗ = (9.75, 6.75, -6.5, -3.75, 2).
4. Three workers
Three workers A, B, C have to work on a specific task. Workers A and B completed whole task in 14 days, B together with C for 23 days, A together with C for 13 days. How long it would take to complete the task every one of them alone? How long it would.
5. XY triangle
Determine area of triangle given by line 7x+8y-69=0 and coordinate axes x and y.
6. Spherical segment
Spherical segment with height h=6 has a volume V=134. Calculate the radius of the sphere of which is cut this segment.
7. Steamship
Between the two ports on the river is going steamship. The journey there and back takes 8:42. Downstream steamship traveling at 20 km/h, upstream 9 km/h. What is the distance between the ports?
8. Blueberries
Marie earns 3 liters of blueberries for 3.4 hours, Peter 2.4 liters for 2.9 hours. How long have earns together one liter?
9. Heron backlaw
Calculate missing side in a triangle with sides 17 and 34 and area 275.
10. Coin and die
Flip a coin and then roll a six-sided die. How many possible combinations are there?
11. Leveling
Calculate how many 25 kg bags of leveling concrete must be purchased if we leveling room 15 m2 to the "height" 6 mm if consumtion is 1.5 kg per square meter and millimeter thickness.
12. Tractors
Six tractors plowing the field for 8 days. After two days, two tractors broke down. How many days were prolonged work in the field?
13. Slope of the pool
Calculate slope (rise:run) of the bottom of swimming pool long 10 m. Water depth at beginning of pool is 1.16 m (for children) and depth at end is 1.89 m (for swimmers). Slope express as percentage and as angle in degrees.
14. Drunk man
Drunkman has 2.6‰ of alcohol in the blood. How many grams of alcohol has in blood, if he have 5 kg of blood?
15. Wheat
The rectangle shaped field with dimensions 889 m and 1336 m harvested last year was 6235 q wheat. (1 q = 1 quintal = 100 kg). During the year, it was necessary to fix the pipe and therefore did kick wide 3 m parallel to the side of the field 1336 m, where.
16. Hexagonal prism
The base of the prism is a regular hexagon consisting of six triangles with side a = 12 cm and height va = 10.4 cm. The prism height is 5 cm. Calculate the volume and surface of the prism!
17. Divisibility
Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16.
18. Shooter
The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot?
19. Wiring
Conduit has a cross section 482 mm. Maybe put it into 6 conductors with a cross section S2 \$mm2?
20. Mystery of stereometrie
Two regular tetrahedrons have surfaces 88 cm2 and 198 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.

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