# Units - examples - page 14

1. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
2. Cut and cone
Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.
3. Inheritance
After death father (♱ 62) remained mother (his wife) and its 3 children. Inheritance by law is that in first mother will automatically get half of the property and other one half inherite by heirs witch are mother and her 3 children by same share. Cal
4. Jewel
Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
5. Clock
What time is now, if the time elapsed after noon is 2/10 of time that elapses before midnight?
6. Solidarity
Imagine a word solidarity means that salt donation to the needy, who have neither the salt. If we take word solidarity has word base salt + gift (only in Slovakian language). Calculate how many kilos of salt sympathetic citizen "gives" government a year i
7. Prism
The base of the prism is a rhombus with a side 30 cm and height 27 cm. The height of the prism is 180% longer than the side length of the rhombus. Calculate the volume of the prism.
8. Stock market
Simon one day decided to invest € 62000 to the stock market. After six months he invested July 25 stock markets fell by 47%. Fortunately for Simon from July 25 5 to October 25 his shares have risen by 39%. Simon is then: ?
9. Pillar
Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48.
10. Rectangles
Calculate how many squares/rectangles of size 4×3 cm can be cut from a sheet of paper of 36 cm × 32 cm?
11. Circle and angle
What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad?
12. Painter Pavel
Painter Pavel painted the fence for 16 hours and painter Petr the same fence painted for 13 h. How long should take painted the fence together?
13. Aquarium
Aquarium is rectangular box with square base containing 76 liters of water. Length of base edge is 42 cm. To what height the water level goes?
14. Tea blend
Tea blends are maked from two kinds of tea. In standard tea mixture are two teas in the ratio 1:3 and 40 g costs 42 CZK. In the premium tea mixture are weighing two teas in the ratio 1:1 and 50 grams costs 60 CZK. How much cost 10 grams of more expensive k
15. Rhomboid
Calculate the circumference and area of the rhomboid with sides 20 and 10, with their angle 20°.
16. Balls
Ping pong balls have a diameter of approximately 4.6 cm. They are sold in boxes of 4 pieces: each box has the shape of a cuboid with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled w
17. Aircraft
If an airplane flies 776 km/h for 7.4 h, how far does it travel?
18. Cycling
Cyclist goes on a trip. First, drove 4 hours average speed 44 kilometers per hour, then slowed down and another 4 hours driving a speed 36 kilometers per hour. How many total kilometers cycling?
19. Discounts on rail (ZSSK)
The railway company ZSSK offers a discount of 15% (REGIONAL) for 5 Eur/year. Calculate the real discount rate as a percentage, where passengers will travel 19 Eur per week.
20. Slope
What is the slope of a line with an inclination -221°?

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