# Examples for 9th grade - page 9

- Pyramid roof

1/3 of area of the roof shaped regular tetrahedral pyramid with base edge 10 m and height of 4 m is already covered with roofing. How many square meters still needs to be covered? - Cylinder - basics

Cylinder with base radius r = 37 cm and height h=74 cm. Calculate: - 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 128 mm. - Ships

At 15:20 the ship set sail at 16 km/h. At 17:50 followed by at 41 km/h sail boat. When sail boat catches up the ship? How many minutes will catch up took? - Roller

Cylinder shell has the same content as one of its base. Cylinder height is 25 m. What is the radius of the base of the cylinder? - Climb in percentage

The height difference between points A and B is 442 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 6.8 km. - Rotary cone

The volume of the rotation of the cone is 104 cm^{3}and angle between the side of the cone and base angle is 80°. Calculate lateral surface area of this cone. - 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 7 cm. - Hollow sphere

Calculate the weight of a hollow brass sphere (density 8.5 g/cm^{3}), if the outer diameter is 10 cm and wall thickness is 3 mm. - Profitable bank deposit 2012

Calculate the value of what money lose creditor with a deposit € 7700 for 4 years if the entire duration are interest 2.2% p.a. and tax on interest is 19% and annual inflation is 3.6% (Calculate what you will lose if you leave money lying idle at negative - Tower

How many m^{2}of copper plate should be to replace roof of the tower conical shape with diameter 13 m and the angle at the vertex of the axial section is 150°? - Diagonals of the rhombus

Calculate height of rhombus whose diagonals are 15 cm and 5 cm. - Gold wire

From one gram of gold was pulled wire 1.2 km length. What is it diameter if density of Au is ρ=19.5 g/cm^{3}? - Tourists

From the cottage started first group of tourists at 10:00 AM at speed 4 km/h. The second started after them 39 minutes later at speed 6 km/h. How long and how many kilometers from the cottage will catch the first group? - Hexagon A

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

How long should be the minimum radius of the circular plate to be cut equilateral triangle with side 7 mm from it? - 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 50 degrees, |AB| = 5 cm. Calculate the volume of the prism. - Road

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

Circular cone with height h = 11 dm and base radius r = 4 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume. - Right isosceles

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

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