# Examples for 8th grade - page 11

- 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. - Cylinder - basics

Cylinder with base radius r = 45 dm and height h=22 dm. Calculate: - 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. - 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 21 cm. - 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. - 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? - 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°? - Diagonals of the rhombus

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

Calculate two positive numbers that its ratio is 6:6 and difference was 0. - 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? - 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. - 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 - 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 30 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. - Bicycle wheel

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

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