# The most difficult examples - page 4

1. Surface area of cylinder
Determine the lateral surface of the rotary cylinder which is circumscribed cube with edge length 5 cm.
2. Energy
In one region, the September energy consumption levels for single-family homes are found to be normally distributed with a mean of 1050 kWh and a standard deviation of of 218 kWh. Find the consumption level separating the bottom 45% from the top 55%.
3. Vector 7
Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
4. Scouts
Scouts purchased for camp cans two types total cost 1460 CZK. First cans were for CZK 32 and second for 25 CZK. How many cans purchased each type?
5. 6 regular polygon
It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm2 (square centimeters) has a circle in which is inscribed the 6-gon.
6. Land - isosceles trapezoid
Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.
7. Triangular prism
Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 22 degrees, |AB| = 6 cm. Calculate the volume of the prism.
8. The cellar
Mr Novák has a cellar and a cellar window in the chalet has 0.6 meter square window. The window wishes to place an X-shaped grid in a square. He uses iron welded bars. Calculate the lengths of individual bars and what the total length of the bars he has t
9. Paper collecting
At the paper collecting contest gathered Franta 2/9 ton, Karel 1/4 ton and Patrick 19/36 tons of paper. Who have gathered the most and the least (x, y - write down the weights in tonnes).
10. Church tower
Archdeacon church in Usti nad Labem has diverted tower by 186 cm. The tower is 65 m high. Calculate the angle by which the tower is tilted. Result write in degree's minutes.
11. Cone and the ratio
Rotational cone has a height 23 cm and the ratio of the base surface to lateral surface is 7: 9. Calculate a surface of the base and the lateral surface.
What is the diameter of a tree around which is 3m 9dm 7cm long rope wrapped? How big is its cross-sectional area?
13. Sebastian
From Kovalov Sebastian walks at 6 km / h started at 8:00 in the direction of Kuty. From Kuty, the godfather is driving at 50 km/h and started at 8:30. The distance is 24 km. When and where grandfather will take Sebastian to the car.
14. Trapezium internal angles
A trapezium where AB is parallel to CD, has angle A : angle D = 4 :5, angle B = 3x-15 and angle C = 4x+20. Find angle A, B, C and D.
15. Axial section
Axial section of the cylinder has a diagonal 40 cm. The size of the shell and the base surface are in the ratio 3:2. Calculate the volume and surface area of this cylinder.
16. Tailor 5
A tailor uses 13/4m of cloth to stitch a skirt. How many metres of cloth is needed to stitch 16 skirts?
17. Engine pulley
The engine has a 1460 rev / min (RPM). Disc diameter is 350 mm. What will be the disc peripheral speed in RPM? Pulleys on the engine has diameter 80mm, on a disc has diameter 160mm.
18. V-belt
Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
19. Unknown number
I think number. If subtract from the twelfth square the ninth square I get a number 27 times greater than the intended number. What is this unknown number?
20. More money
Lenka has €4.8 more than Natalia. Who will have more and how much, when Lenka give Natalia €2.5?

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