# Examples for 9th grade - page 55

- Office

Office building was built in the shape of a regular hexagon inscribed in a circle with a radius of 12 m. The height of the walls is 7m. How much CZK cost plastering the walls of the building, if per 1 m square cost CZK 400? - Friends

Some friends had to collect the sum 72 EUR equally. If the three refused their part, others would have to give each 4 euros more. How many are friends? - 4side pyramid

Calculate the volume and surface of 4 side regular pyramid whose base edge is 4 cm long. The angle from the plane of the side wall and base plane is 60 degrees. - Chimney

Lower circumference of of the chimney is 12.57 m, top circumference is 5.655 m. The slope of the walls is 87°. Determine the height of the chimney. - Cube from sphere

What largest surface area (in cm^{2}) can have a cube that was cut out of a sphere with radius 3 cm? - Clock

What distance will pass end of 8 cm long hour hand for 15 minutes? - Dollars

Mama split 760 dollars Jane, Dane and Eva as follows: Jane got three times more than Dane and Dane and got 40 more than Eva. How much does get each of them? - Two boxes-cubes

Two boxes cube with edges a=74 cm and b = 91 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge? - Silver medal

To circular silver medal with a diameter of 10 cm is inscribed gold cross, which consists of five equal squares. What is the content area of silver part? - Sphere area

A cube with edge 1 m long is circumscribed sphere (vertices of the cube lies on the surface of a sphere). Determine the surface area of the sphere. - 3 years

The company has increased the number of employees. In year 1997 compared to 1996 17% more, in 1998 12% more against the previous year, in year 1999 20% more compared to 1998. How many % increase in the number of employees in 3 years? - Paper box

Calculate the consumption of paper on the box-shaped quadrangular prism with rhombic footstall, base edge a=6 cm and the adjacent base edges forms an angle alpha = 60 °. Box height is 10 cm. How many m^{2}of the paper consumed 100 such boxes? - Surface area

The volume of a cone is 1000 cm^{3}and the content area of the axis cut is 100 cm^{2.}Calculate the surface area of the cone. - 3 days

Worker checked 2,950 products in 3 days. Second day checked 25% more than the first day. The third day 15% more products than the second day. How many products he checked in each day. - Chord 3

What is the radius of the circle where the chord is 2/3 of the radius from the center and has a length of 10 cm? - Trapezoid RT

The plot has a shape of a rectangular trapezium ABCD, where ABIICD with a right angle at the vertex B. side AB has a length 36 m. The lengths of the sides AB and BC are in the ratio 12:7. Lengths of the sides AB and CD are a ratio 3:2. Calculate consumptio - Orchard

Route passes trapezoidal orchard perpendicular to the parallel sides. It is 80 cm wide. The lengths of the bases are in the ratio 5:3 and the length of the longer base to the length of the path is in the ratio 5:6. How many square meters occupies the rou - Chemical parison

The blown parison (with shape of a sphere) have a volume 1.3 liters. What is its surface? - Antennas

If you give me two antennas will be same. If you give me again your two antenna I have a 5× so many than you. How many antennas have both mans? - Profits

Two members will make profit 52 000, - EUR. The forst earned 8% more and the second 10% more and thus earned together 56 700, - EUR. How many will initially each earn?

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