# Examples for 9th grade - page 10

- Hexagon A

Calculate area of regular hexagon inscribed in circle with radius r=7 m. - Road

Between cities A and B is route 3 km long of rise average 4‰. Calculate the height difference of cities A and B. - Right isosceles

Calculate area of the isosceles right triangle which perimeter is 35 cm. - Balls

Three metal balls with volumes V_{1}=41 cm^{3}V_{2}=58 cm^{3}and V_{3}=83 cm^{3}melted into one ball. Determine it's surface area. - Similarity coefficient

The ratio of similarity of two equilateral triangles is 3.9 (ie 39:10). The length of the side of smaller triangle is 3 cm. Calculate the perimeter and area of the larger triangle. - Team

The football team has 11 players. Their average age is 21 years. During the match due to injury, one player withdraws and the average age of the team is 20. How old was injured player? - Axial section

Axial section of the cylinder has a diagonal 63 cm long and we know that the area of the side and the area of base is in ratio 1:3. Calculate the height and radius of the cylinder base. - Hole

In the center of the cube with edge 15 cm we will drill cylinder shape hole. Volume of the hole must be 28% of the cube. What drill diameter should be chosen? - Tinsmith

Tinsmith construct chimney pipe 126 cm long and 11 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? - Radius

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

Rudolf decided to take the train from the station 'Nová Baňa' to 'Gelnica'. In the train timetables found train R 371 Horehronec : km0Břeclav os.n.05:268Lanžhot05:3205:3214Brodské05:3705:3818Kúty05:4205:4344Malacky05:5906:0082Bratislava hl.st.06:2606:37 - Diofant 2

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

Product has been discounted twice by 14%. What is the total discount given? - Shelf

How many ways are there to arrange 9 books on a shelf? - Cu wire

Copper wire has a length l = 210 m and diameter d = 10 mm. Calculate the weight if density of copper is ρ = 8500 kg/m^{3.}Result round to one decimal place. - Parquet floor

Three workers laid parquet floor for 1.957 hour. The first one would do this work alone 5 hours, the second in 9 hours. For how many hours would fulfill this work the third worker, if he worked alone? - Rhombus 2

Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long. - Cuboid

Determine the dimensions of cuboid a, b, c; if diagonal d=6 dm has angle with edge a α=57° and has angle with edge b β=60° - Madams

During the spring cleaning ladies going to wash windows. Mother takes wash all the windows 5 hours, the grandmother 3 times longer and Paula wash all windows in 5 hours. How many hours will spend washing the windows this "women's team" if working togethe - Cubes

Cube, which consists of 27 small cubes with edge 3 dm has volume:

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