# Examples for 8th grade - page 62

- Paul and Honza

Honza went to chat on a bike without a break 3.0 hours. Paul the same way without breaks 30 minutes longer. The difference between the speeds of the two boys was the one kilometer per hour. How fast was Paul, if you know that the speed of the boys did not. - Wheel

What is the wheel diameter if on the 0.42 km track turns 115 times? - The body

The body on the figure consists of cubes with an edge length 10 cm. What surface has this body? - Trousers

Jarek bought new trousers, but the trousers were too long. Their length was in the ratio 5: 8 to Jarek height. Mother his trousers cut by 4 cm, thus the original ratio decreased by 4%. Determine Jarek's high. - Sinus

Determine the smallest integer p for which the equation 5 sin x = p has no solution. - Pigs

Pigs are feed by beet.Beet feed containing 12% dry solids, which is 0.66% of digestible crude protein. How much beet must beconsumed in one month (30 days), if the weight of digestible crude protein contained in a daily dose of beet was 0.688 kg? - Aircrafts

Above the town hall tower flew the plane with constant speed 508 km/h and 15 minutes later the second plane at speed of 651 km/h. How long and how far from the town hall will be aircrafts caught up? - Inscribed rectangle

The circle area is 184. Determine the area of inscribed rectangle with one side 10 long. - ISO trapezium

Calculate area of isosceles trapezoid with base 53 long, leg 43 long and with the angle between the base and leg 70 degrees. - Ethnicity

Share of ethnicity XY is 10%, which is 1/9 more than in the prewar period. What was the share of that ethnicity in the pre-war period? - Circle section

Equilateral triangle with side 50 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. - Three workers

Three workers A, B, C have to work on a specific task. Workers A and B completed whole task in 25 days, B together with C for 16 days, A together with C for 10 days. How long it would take to complete the task every one of them alone? How long it would. - Icerink

Rectangular rink with dimensions of 79.5 m and 529 dm must be covered with a layer of ice 4.5 cm thick. How many liters of water is necessary for the formation of ice when the volume of ice is 10.9% greater than the volume of water. - Tower

How many m^{2}of copper plate should be to replace roof of the tower conical shape with diameter 13 m and the angle at the vertex of the axial section is 150°? - Silo

Outer perimeter of silo is 24 m. Concrete wall is 18 cm thick. What is diameter and area of inside floor of silo? - Prism

Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 5 cm has same volume as a cube with an edge length of 1 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube' - Sines

In ▵ ABC, if sin(α)=0.5 and sin(β)=0.1 calculate sin(γ) - Steamship

Between the two ports on the river is going steamship. The journey there and back takes 14:49. Downstream steamship traveling at 21 km/h, upstream 9 km/h. What is the distance between the ports? - Parallelogram

Calculate area of the parallelogram ABCD as shown if |AB| = 45 cm, |BC| = 23 cm and angle BAD = 30° - Triangle ABC

Calculate the sides of triangle ABC with area 883 cm^{2}and if a: b: c = 15:7:19

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