# Examples for secondary school students - page 14

- Coin and die

Flip a coin and then roll a six-sided die. How many possible combinations are there? - Spherical segment

Spherical segment with height h=6 has a volume V=134. Calculate the radius of the sphere of which is cut this segment. - Geometric progression

Fill 4 numbers between 4 and -12500 to form geometric progression. - Slope of the pool

Calculate slope (rise:run) of the bottom of swimming pool long 10 m. Water depth at beginning of pool is 1.16 m (for children) and depth at end is 1.89 m (for swimmers). Slope express as percentage and as angle in degrees. - Shooter

The shooter fired to a target from distance 11 m The individual concentric circle of targets have a radius increments 1 cm (25 points) by 1 point. Shot was shifted by 8'(angle degree minutes). How many points should win his shot? - Wiring

Conduit has a cross section 48^{2}mm. Maybe put it into 6 conductors with a cross section S2 $mm^{2}? - Divisibility

Determine the smallest integer which divided 11 gives remainder 4 when divided 15 gives remainder 10 and when divided by 19 gives remainder 16. - Mystery of stereometrie

Two regular tetrahedrons have surfaces 88 cm^{2}and 198 cm^{2}. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places. - Nine-gon

Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm. - 3y inflation

Price of the roll rise in the first year by 9%, the second year fell by 5% and in the third year increased by 3%. Calculate the average annual increase in price of the roll. - Sphere and cone

Within the sphere of radius G = 33 cm inscribe cone with largest volume. What is that volume and what are the dimensions of the cone? - Side c

In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c. - Black building

Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m^{2}for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchin - Pit

Pit has shape of a truncated pyramid with rectangular bases and is 0.8 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.6 l of green colour. How many liters of paint is needed when w - Road

Average climb of the road is given by ratio 1:15. By what angle road average climb? - Lock

Combination lock will open when the right choice of 3 numbers (from 1 to 25 inclusive) is selected. A. How many different lock combinations are possible? B. Is he combination lock named appropriately? - Circle

From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x_{0}, y_{0}] and radius of the circle r. - AVG of INT

What is the average of the integers from 9 throuht 52 inclusive? - Height difference

What height difference overcome if we pass road 1 km long with a pitch21 per mille? - Elevation

What must be the elevation of an observer in order that he may be able to see an object on the earth 782 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.

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