# Units - examples - page 16

1. Goat and circles
What is the radius of a circle centered on the other circle and the intersection of the two circles is equal to half the area of the first circle? This task is the mathematical expression of the role of agriculture. The farmer has circular land on which g
2. Plan of the village
Plan of the municipality in 1:1000 scale has plotted garden with dimensions 25 mm and 28 mm. Determine the area of gardens in ares in reality.
3. Water
Into a full cylindrical tank high 3.6 with base radius 2.3 m we insert cuboid with dimensions 0.5 m, 1.9 m, 0.7 m. How many liters of water will come out?
4. Tetrahedral pyramid
Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm2 and deviation angle of the side edges from the plane of the base is 60 degrees.
5. Motion
From two different locations distant 232 km started against car and bus. The car started at 5:20 with average speed 64 km/h. Bus started at 7:30 with average speed 80 km/h. When they meet? How many kilometers went the bus?
6. Sale
If the product twice price cut by 25%, what percentage was price cut in total?
7. Peroxide
How much distilled water (in liters) must pharmacists pour into 300 ml of 23.6% solution of hydrogen peroxide to get 2.7% solution to gargle?
8. Circle section
Equilateral triangle with side 33 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector.
9. Triangular pyramid
Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm.
10. 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.
11. The chord
Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°?
12. Angle between vectors
Find the angle between the given vectors to the nearest tenth of a degree. u = (-22, 11) and v = (16, 20)
13. 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
14. Jewel
Rhombus-shaped jewel have area of 93 mm2 and the edge in long 13.2 mm. Calculate the size of rhombus acute angle.
15. Clock
What time is now, if the time elapsed after noon is 4/15 of time that elapses before midnight?
16. 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
17. 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.
18. Rectangles
Calculate how many squares/rectangles of size 4×3 cm can be cut from a sheet of paper of 36 cm × 32 cm?
19. 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.
20. Circle and angle
What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad?

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