# Examples for 8th grade - page 11

- Cone

Circular cone with height h = 29 dm and base radius r = 3 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume. - Tourists

From the cottage started first group of tourists at 10:00 AM at speed 4 km/h. The second started after them 47 minutes later at speed 6 km/h. How long and how many kilometers from the cottage will catch the first group? - Triangular prism

Plane passing through the edge AB and the center of segmet CC' of regular triangular prism ABCA'B'C', has angle with base 39 degrees, |AB| = 3 cm. Calculate the volume of the prism. - Diagonals of the rhombus

Calculate height of rhombus whose diagonals are 12 cm and 19 cm. - Garden

Father dig up the garden in 9 hours. Son in 13 hours. How many hours take dig up the garden together? - Prism

Three cubes are glued into prism, sum of the lengths of all its edges is 115 cm. What is the length of one edge of the original cube? - Tower

How many m^{2}of copper plate should be to replace roof of the tower conical shape with diameter 24 m and the angle at the vertex of the axial section is 144°? - Rhombus 2

Calculate the area of rhombus which has a height v=48 mm and shorter diagonal u = 60 mm long. - Profitable bank deposit 2012

Calculate the value of what money lose creditor with a deposit € 9500 for 4 years if the entire duration are interest 2.6% p.a. and tax on interest is 19% and annual inflation is 3.7% (Calculate what you will lose if you leave money lying idle at negative - Bicycle wheel

Bicycle wheel has a diameter of 70 cm. Approximately how many times the wheel rotates at 4.7 km long trip? - Equilateral triangle

How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 7 mm from it? - Cube

The cube weighs 24 kg. How weight is cube of the same material, if its dimensions are 2-times smaller? - 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. - Number ratio

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

How many ways are there to arrange 6 books on a shelf? - 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 7 km long of fall average 4‰. Calculate the height difference of cities A and B.

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