The most difficult examples - page 4
- Surface area of cylinder
Determine the lateral surface of the rotary cylinder which is circumscribed cube with edge length 5 cm.
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%.
- Vector 7
Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|.
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?
- 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.
- 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.
- 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.
- 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
- 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).
- 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.
- 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.
- Tree shadow 3
What is the diameter of a tree around which is 3m 9dm 7cm long rope wrapped? How big is its cross-sectional area?
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.
- 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.
- 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.
- Tailor 5
A tailor uses 13/4m of cloth to stitch a skirt. How many metres of cloth is needed to stitch 16 skirts?
- 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.
Calculate a length of the V-belt when the diameter of the pulleys is: D1 = 600 mm D2 = 120 mm d = 480 mm
- 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?
- More money
Lenka has €4.8 more than Natalia. Who will have more and how much, when Lenka give Natalia €2.5?