# Examples for secondary school students

1. Cone container
Rotary cone-shaped container has a volume 1000 cubic cm and a height 12 cm. Calculate how much metal we need for making this package.
2. Controller
Output Controller of the company in the control of 50 randomly selected products found that 37 of them had no defect 8 has only one flaw, three had two defects, and two products had three defects. Determine the standard deviation and coefficient of variat
3. Prism
The base of a perpendicular triangular prism is a right triangle with legs 4.5 cm and 6 cm long. What is the surface of the prism, if its volume is 54 cubic centimeters?
4. Numbers at ratio
The two numbers are in a ratio 3:2. If we each increase by 5 would be at a ratio of 4:3. What is the sum of original numbers?
5. Hexagon = 8 parts
Divide the regular hexagon into eight equal parts.
6. Trapezium ABCD
In the figure, ABDC is a trapezium in which AB || CD. line segments RN and LM are drawn parallel to AB such that AJ=JK=KP. If AB=0.5m and AP=BQ=1.8m, find the lengths of AC, BD, RN and LM. angle D=angle C=60
7. Volume of three cuboids
Calculate the total volume of all cuboids for which the the size of the edges are in a ratio of 1:2:3, and one of the edges has a size 6 cm.
8. Triangle KLB
It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area
9. Desribed circle to rectangle
Rectangle with sides 6 cm and 4 cm was circumscribed circle. What part of the content of the circle determined by the circumscribed circle occupies a rectangle? Express in perctentages(%).
10. AP - simple
Find the first ten members of the sequence if a11 = 132, d = 3.
11. Decagon prism
A regular decagon of side a = 2 cm is the base of the perpendicular prism, the side walls are squares. Find the prism volume in cm3, round to two decimal places.
12. Ring
The ring made from gold and copper alloy has a weight of 14.5 g and a volume of 1.03 cm3. How much gold and how much copper it contains? The metal densities are Au 19.3 g/cm³ and Cu 8.94 kg·dm-3
In six baskets, the seller has fruit. In individual baskets, there are only apples or just pears with the following number of fruits: 5,6,12,14,23 and 29. "If I sell this basket," the salesman thinks, "then I will have just as many apples as a pear." Whic
14. Freezer
The freezer has the shape of a cuboid with internal dimensions of 12 cm, 10 cm, 30 cm. A layer of ice of 23 mm thick was formed on the inner walls (and on the opening) of the freezer. How many liters of water will drain if we dispose the freezer?
15. Two lands
The common area of the two neighboring lands is 964 m2. The second land is 77 m2 smaller than twice the size of the first land. Find the areas of each land.
16. Men, women and children
On the trip went men, women and children in the ratio 2:3:5 by bus. Children pay 60 crowns and adults 150. How many women were on the bus when a bus was paid 4,200 crowns?
17. AP - simple
Determine the first nine elements of sequence if a10 = -1 and d = 4
18. Quatrefoil
Calculate area of the quatrefoil which is inscribed in a square with side 6 cm.
19. Vertical prism
The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism
20. Two balls
Two balls, one 8cm in radius and the other 6cm in radius, are placed in a cylindrical plastic container 10cm in radius. Find the volume of water necessary to cover them.

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