# Examples for 8th grade - page 35

- Shadow and light

Nine meters height poplar tree has a shadow 16.2 meters long. How long shadow have at the same time Joe if he is 1,4m tall? - Water tank 2

Water tank cuboid is 12 meters long and 6.5 meters wide and 1.2 meters high. How many hectoliters are in the tank when it is filled to 81%? - Rectangular triangles

The lengths of corresponding sides of two rectangular triangles are in the ratio 2:5. At what ratio are medians relevant to hypotenuse these right triangles? At what ratio are the contents of these triangles? Smaller rectangular triangle has legs 6 and 8 c - angles in quadrilateral

What size have angles in quadrilateral (4-gon) if they are in a ratio of 8: 9: 10: 13? - Logik game

Letter game Logik is a two player game, which has the following rules: 1. The first player thinks five-letter word in which no letter is not repeated. 2. The second player writes a five-letter word. 3. The first player answers two numbers - the first numbe - Surface area

The volume of a cone is 1000 cm^{3}and the content area of the axis cut is 100 cm^{2}. Calculate the surface area of the cone. - Passenger car

Passenger car travels 1 km for 2.3 minutes, a truck during a 50 seconds long. How much is the speed of the truck less? - A family

A family of four pays for garbage collection per year 1800 Kč. How many crowns a year the waste company get from the house where lives 93 people? - ICE train

German runways test a new ICE train between Munich and Berlin. The train runs to Berlin at a slow speed of 100 km/h. Back from Berlin goes faster. How quickly did the train have to go on a return trip so that the total average train speed for both journeys - Minute-hand

How long distance will travel a large (minute) hand on the clock for 47 minutes, if its length is 43 cm? - Unknown integer

Find the smallest integer that: divided by 2, the remainder is 1 divided by 3 the remainder is 2, divided by 4 remainder is 3, ... divided by eight reminder is 7, by 9 reminder is 8. - Ascent and descent

Car goes 114 km track, which consists of ascent and descent at time of 1 hour 35 minutes. When climbing moves at the speed 48 km/h and downhill 25 m/s. What is the length of climb and descent? - Spartakiada

Practitioners lined up in rectangle with row with four, five or six exercisers, one always missing to full rectangle. How many exercisers were on the field, if they have estimated not been more than 100? - Bricks wall

There are 5000 bricks. How high wall thickness of 20 cm around the area which has dimensions 20 m and 15 m can use these bricks to build? Brick dimensions are 30 cm, 20 cm and 10 cm. - Painting

Jožko with Fero painted the bench for four hours. How many hours would take work if four friends help him? - Angles of the triangle

ABC is a triangle. The size of the angles alpha, beta are in a ratio 4: 7. The angle gamma is greater than the angle alpha by a quarter of a straight angle. Determine angles of the triangle ABC. - Tournament

Determine how many ways can be chosen two representatives from 34 students to school tournament. - Disinfecting solution

How much distilled water is necessary to pour into 500 ml of 33% hydrogen peroxide solution to obtain 3% disinfecting solution? - Painters

The first team of painters would paint bridge in 15 days, the second in 10 days. After 3 days of working together second team goes out and continue only first team. How many days took second team to finish painting the bridge? - Reflector

Circular reflector throws light cone with a vertex angle 49° and is on 33 m height tower. The axis of the light beam has with the axis of the tower angle 30°. What is the maximum length of the illuminated horizontal plane?

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