# Examples for 9th grade - page 10

- 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. - Cylinder - basics

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

Calculate perimeter and area of a triangle ABC, if a=40, b=36 and c=36. - 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? - 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. - Rotary cone

The volume of the rotation of the cone is 472 cm^{3}and angle between the side of the cone and base angle is 70°. Calculate lateral surface area of this cone. - 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 22 degrees, |AB| = 6 cm. Calculate the volume of the prism. - 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? - Diagonals of the rhombus

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

Cylinder shell has the same content as one of its base. Cylinder height is 15 dm. What is the radius of the base of the cylinder? - 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°? - Shelf

How many ways are there to arrange 6 books on a shelf? - 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 - Equilateral triangle

How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 19 cm from it? - Ships

At 8:40 the ship set sail at 12 km/h. At 19:10 followed by at 29 km/h sail boat. When sail boat catches up the ship? How many minutes will catch up took? - Hexagon A

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

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