# Examples for 8th grade - page 12

- Hexagon A

Calculate area of regular hexagon inscribed in circle with radius r=9 cm. - Similarity coefficient

The ratio of similarity of two equilateral triangles is 3.5 (ie 7:2). The length of the side of smaller triangle is 2.4 cm. Calculate the perimeter and area of the larger triangle. - Shelf

How many ways are there to arrange 6 books on a shelf? - Number ratio

Calculate two positive numbers that its ratio is 6:6 and difference was 0. - Balls

Three metal balls with volumes V_{1}=71 cm^{3}V_{2}=78 cm^{3}and V_{3}=64 cm^{3}melted into one ball. Determine it's surface area. - Team

The football team has 11 players. Their average age is 20 years. During the match due to injury, one player withdraws and the average age of the team is 18. How old was injured player? - Diofant 2

Is equation ? solvable on the set of integers Z? - Road

Between cities A and B is route 13 km long of stúpanie average 7‰. Calculate the height difference of cities A and B. - Speed of Slovakian trains

Rudolf decided to take the train from the station 'Trnava' to 'Zemianske Kostoľany'. In the train timetables found train R 725 Remata : km0Bratislava hl.st.12:574Bratislava-Vinohrady13:0113:0219Pezinok13:1213:1346Trnava13:3013:3263Leopoldov13:4514:0168H - Metallurgical enterprise

Metallurgical company daily produces 318 tons of cast iron. How many tons of coke it burns to melt cast iron when 10 tons of cast consumes 6 tons of coke? - Right isosceles

Calculate area of the isosceles right triangle which perimeter is 49 cm. - Plumber

Plumber had to cut the metal strip with dimensions 380 cm and 60 cm to the largest squares so that no waste. Calculate the length of the sides of a square. How many squares cut it? - Hole

In the center of the cube with edge 14 cm we will drill cylinder shape hole. Volume of the hole must be 27% of the cube. What drill diameter should be chosen? - Air

Room is 40.1 m long, 25.2 dm wide and 369 cm high. How many people can simultaneously be in this room if for hygiene reasons is calculated 5100 dm^{3}of air per person? - Parquet floor

Three workers laid parquet floor for 2.9 hour. The first one would do this work alone 9 hours, the second in 7 hours. For how many hours would fulfill this work the third worker, if he worked alone? - Tinsmith

Tinsmith construct chimney pipe 145 cm long and 15 cm wide. What are the dimensions of the sheet will have to prepare for the construction of a pipe when the plate overlap at the joint add $x cm width of the plate? - Cu wire

Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m^{3}. Result round to one decimal place. - Pool

Mr. Peter build a pool shape of a four-sided prism with rhombus base in the garden. Base edge length is 8 m, distance of the opposite walls of the pool is 7 m. Estimated depth is 144 cm. How many hectoliters of water consume Mr. Peter to fill the pool? - Radius

Determine the radius of the circle, if its perimeter and area is the same number. - Discount

Product has been discounted twice by 19%. What is the total discount given?

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