# Examples for secondary school students - page 11

1. Pillar
Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48.
2. Stock market
Simon one day decided to invest € 62000 to the stock market. After six months he invested July 25 stock markets fell by 47%. Fortunately for Simon from July 25 5 to October 25 his shares have risen by 39%. Simon is then: ?
3. Circle and angle
What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad?
4. Painter Pavel
Painter Pavel painted the fence for 16 hours and painter Petr the same fence painted for 13 h. How long should take painted the fence together?
5. Tea blend
Tea blends are maked from two kinds of tea. In standard tea mixture are two teas in the ratio 1:3 and 40 g costs 42 CZK. In the premium tea mixture are weighing two teas in the ratio 1:1 and 50 grams costs 60 CZK. How much cost 10 grams of more expensive k
6. Balls
Ping pong balls have a diameter of approximately 4.6 cm. They are sold in boxes of 4 pieces: each box has the shape of a cuboid with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled w
7. Slope
What is the slope of a line with an inclination -221°?
8. Cylinder - A&V
The cylinder has a volume 1287. The base has a radius 10. What is the area of surface of the cylinder?
9. Circle
Circle touch two parallel lines p and q; and its center lies on a line a, which is secant of lines p and q. Write the equation of circle and determine the coordinates of the center and radius. p: x-10 = 0 q: -x-19 = 0 a: 9x-4y+5 = 0
10. Steeple
Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?
11. Playing cards
How many possible ways are to shuffle 7 playing cards?
12. KLMN
In the trapezoid KLMN is given this informations: 1. segments KL and MN are parallel 2. segments KL and KM has same length 3. segments KN, NM and ML has same length. Determine the size of the angle KMN.
13. Sugar - cuboid
Pejko received from his master cuboid composed of identical sugar cubes with count between 1000 and 2000. The Pejko eat sugar cubes in layers. The first day eat one layer from the front, second day one layer from right, the third day one layer above. Yet i
14. Wood in the forest
The amount of wood in the forest was estimated at 6000 m3. How much wood will be in forest after 2 years if the annual growth of wood is 2.5% each year and logging 30 m3 each year?
15. Pyramid
Pyramid has a base a = 5cm and height in v = 8 cm. a) calculate angle between plane ABV and base plane b) calculate angle between opposite side edges.
16. Free fall
Lloyd fall from height 7 m. Calculate the speed he hit the ground when falling with acceleration g = 9.81 m/s2
17. n-gon
What is the side length of the regular 5-gon inscribed in a circle of radius 12 cm?
18. Reservoir + water
Reservoir completely filled with water weighs 12 kg. After pouring off three quarters of the amount of water weights 3 kg. Calculate the weight and volume of the reservoir.
19. Built-up area
John build up area 5 x 7 = 35 m2 with building with a wall thickness 30 cm. How many centimeters would have to subtract from thickness of the walls that built-up area fell by 9%?
20. Hexagonal pyramid
Calculate the volume and the surface of a regular hexagonal pyramid with a base edge length 3 cm and a height 5 cm.

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