# Examples for 8th grade - page 34

1. Pyramid 8 Calculate the volume and the surface area of a regular quadrangular pyramid with the base side 9 cm and side wall with the base has an angle 75°.
2. Snowman In a circle with a diameter 50 cm are drawn 3 circles /as a snowman/ where: its diameters are integers, each larger circle diameter is 3 cm larger than the diameter of the previous circle. Determine snowman height if we wish highest snowman.
3. 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.
4. Compare II Which of the numbers 710, 107 is greater?
5. Rising price The book first become more expensive by 5 euros. New price was later increased by 8%. After the second price increase book cost 46 euros. What was the original price of the book?
6. 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
7. 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%?
8. 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 What size have angles in quadrilateral (4-gon) if they are in a ratio of 8: 9: 10: 13?
10. Surface area The volume of a cone is 1000 cm3 and the content area of the axis cut is 100 cm2. Calculate the surface area of the cone. 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?
12. 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?
13. 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?
14. 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.
15. Minute-hand How long distance will travel a large (minute) hand on the clock for 47 minutes, if its length is 43 cm?
16. 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
17. 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.
18. 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?
19. Painting Jožko with Fero painted the bench for four hours. How many hours would take work if four friends help him?
20. Tournament Determine how many ways can be chosen two representatives from 34 students to school tournament.

Do you have an interesting mathematical word problem that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...