# The most difficult examples - page 4

- The terrace

Around the round pool with a diameter of 5.5 meters is a wooden terrace with a width of 130 cm. What is the area of the terrace? - Sawmill factory

Peter works in the factory. The bus stop is 10 km from the factory. Therefore, always when the bus arrives for Peter, the driver leaves factory and takes him to work. They are coming at the saw exactly at 8:00. Today the bus arrived 11 minutes earlier and. - Two trains

There are two trains running the same distance. 1st train will travel it in 7 hours 21minutes. 2nd the train will travel 5 hours 57minutes and 34 seconds and it is 14 km/h faster than the first train. What are speeds of trains and how long is this railway - Ladder

4 m long ladder touches the cube 1mx1m at the wall. How high reach on the wall? - Flowerbed

Flowerbed has the shape of a truncated pyramid, the bottom edge of the base a = 10 m, the upper base b = 9 m. Deviation angle between edge and the base is alpha = 45°. What volume is needed to make this flowerbed? How many plants can be planted if 1 m^{2}=. - Cuboid box

How many m^{2}paper is needed for the sticking cuboid box of dimensions 50 cm, 40 cm and 30 cm? To the folds add one-tenth the area. - Dusan

a) Dusan break two same window, which has triangular shape with a length of 0.8 m and corresponding height 9.5 dm. Find how many dm^{2}of glass he needs to buy for glazing of these windows. b) Since the money to fix Dusan has not, must go to the paint job - RTriangle 17

The hypotenuse of a right triangle is 17 cm. If you decrease both two legs by 3 cm you will reduce the hypotenuse by 4 cm. Determine the length of this legs. - Vector 7

Given vector OA(12,16) and vector OB(4,1). Find vector AB and vector |A|. - 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. - 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? - Retail

At what price bought retail 1 kg goods from wholesale, if lost in the distribution is 4% of weight of the goods and retail still have a profit of 6.3%? Goods are sold at retail for 25 euro per kg. - 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 39 degrees, |AB| = 3 cm. Calculate the volume of the prism. - Surface area of cylinder

Determine the lateral surface of the rotary cylinder which is circumscribed cube with edge length 5 cm. - Four friends

Four friends shared the money. Vasek got 1/4 of the total amount. Tonda received 1/3 of the rest of the money, Joe got a half from the second residue and Jirka left 80. How much money get together? - 6 regular polygon

It is given 6 side regular polygon whose side is 5 cm. Calculate its content area. Compare how many more cm^{2}(square centimeters) has a circle in which is inscribed the 6-gon. - Scalene triangle

Solve the triangle: A = 50°, b = 13, c = 6 - Hour salary

You work for 4 hours on a Saturday and 8 hours on Sunday. You also receive a $50 bonus. You earn $164. How much did you earn per hour? - 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 - 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%.

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