# Examples for secondary school students - page 14

1. Wiring
Conduit has a cross section 482 mm. Maybe put it into 6 conductors with a cross section S2 \$mm2?
2. Mystery of stereometrie
Two regular tetrahedrons have surfaces 88 cm2 and 198 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
3. Nine-gon
Calculate the perimeter of a regular nonagon (9-gon) inscribed in a circle with a radius 13 cm.
4. 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?
5. 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.
6. Lock
Combination lock will open when the right choice of 5 numbers (from 1 to 12 inclusive) is selected. A. How many different lock combinations are possible? B. Is he combination lock named appropriately?
7. Side c
In △ABC a=2, b=4 and ∠C=100°. Calculate length of the side c.
8. 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
9. Black building
Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchin
Average climb of the road is given by ratio 1:15. By what angle road average climb?
11. Height difference
What height difference overcome if we pass road 1 km long with a pitch21 per mille?
12. Circle
From the equation of a circle: ? Calculate the coordinates of the center of the circle S[x0, y0] and radius of the circle r.
13. AVG of INT
What is the average of the integers from 9 throuht 52 inclusive?
14. Cuboid
Find the cuboid that has the same surface area as the volume.
15. Elevation
What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
16. Triangle and its heights
Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
17. Dices
We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
18. N-gon
How many diagonals has convex 11-gon?
19. Cinema
Cinema auditorium is built for 3300 people. The first row is planned for 36 seats and each next gradually 4 more. How many rows of seats will have auditorium?
20. Circular sector
I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector?

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