# Examples for 8th grade - page 12

- Gear wheels

Two gear wheels, which fit together have number of teeth z_{1}=72 and z_{2}=200. Calculate the speed of the first wheel, if the second wheel rotates 503 revolutions per minute. - Workers

Two workers fulfill a certain task when working together for 5 days, the first if he worked himself done work in 13 days. How many days will do whole job a second worker? - Pizza

Pizza with a diameter 50 cm have weight 559 g. What diameter will have a pizza weighing 855 g if it is make from the same cloth (same thickness....) and same decorated? - Rhombus

Find the length of the other diagonal and area of rhombus. The perimeter of a rhombus is 40 cm and one of the diagonals is of length 10 cm. - Climb

On the road sign, which informs the climb is 8.7%. Car goes 5 km along this road. What is the height difference that car went? - Cylinder - basics

Cylinder with base radius r = 45 dm and height h=22 dm. Calculate: - Acid

The barrel is 199 litres of 38% acid. How many percent acid occurs when 61 litres revoke and replace it with the same amount of water? - Tetrahedral pyramid

Calculate the volume and surface area of a regular tetrahedral pyramid, its height is $b cm and the length of the edges of the base is 6 cm. - ISO triangle

Calculate the area of an isosceles triangle KLM if the length of its sides are in the ratio k:l:m = 4:4:3 and has perimeter 377 mm. - Tape

Video is 153% more expensive than tape recorder. How many percent is tape recorder less expensive than video? - Hollow sphere

Calculate the weight of a hollow tungsten sphere (density 19.3 g/cm^{3}), if the inner diameter is 14 cm and wall thickness is 3 mm. - 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. - 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°? - 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? - 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? - 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 - Rhombus 2

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

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