# Examples for secondary school students - page 47

1. Gasoline 35 l of gasoline is to be divided into four canisters so that in the third canister was 5 l less than the first canister, the fourth canister 10 l more than in the third canister and the second canister half what in the first canister. How many liters of.
2. Pentagon Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.
3. Water channel The cross section of the water channel is a trapezoid. The width of the bottom is 19.7 m, the water surface width is 28.5 m, the side walls have a slope of 67°30' and 61°15'. Calculate how much water flows through the channel in 5 minutes if the water flow
4. Nuts Peter has 49 nuts. Walnuts have 3 more than hazelnuts and hazelnut 2 over almonds. Determine the number of wallnuts, almonds and hazelnuts.
5. Three friends Divide 570 euros to three friends so that first will get 50 euros less than the second and third twice more than the first. How many euros will get everyone?
6. 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?
7. Billiard balls A layer of ivory billiard balls of radius 6.35 cm is in the form of a square. The balls are arranged so that each ball is tangent to every one adjacent to it. In the spaces between sets of 4 adjacent balls other balls rest, equal in size to the original. T
8. Crystal water The chemist wanted to check the content of water of crystallization of chromic potassium alum K2SO4 * Cr2 (SO4) 3 * 24 H2O, which was a long time in the laboratory. From 96.8 g of K2SO4 * Cr2 (SO4) 3 * 24 H2O prepared 979 cm3 solution of base. S
9. Lines How many lines can be draw with 8 points, if three points lie on one line and the other any three points do not lie on the same line?
10. Variations Determine the number of items when the count of variations of fourth class without repeating is 42 times larger than the count of variations of third class without repetition.
11. Truncated cone 5 The height of a cone 7 cm and the length of side is 10 cm and the lower radius is 3cm. What could the possible answer for the upper radius of truncated cone?
12. 3s prism It is given a regular perpendicular triangular prism with a height 19.0 cm and a base edge length 7.1 cm. Calculate the volume of the prism.
13. Four sided prism Calculate the volume and surface area of a regular quadrangular prism whose height is 28.6cm and the body diagonal forms a 50 degree angle with the base plane.
14. Doctor 2 A doctor noted the Diastolic Blood Pressure (DBP) of a large number of patients. Later, he scrambled the data to keep the privacy of his patients. Based on the scrambled dataset, he finds that the lower inner fence is equal to 50 and the upper inner fenc
15. Roots Determine the quadratic equation absolute coefficient q, that the equation has a real double root and the root x calculate: ?
16. Candies If Alena give Lenka 3 candy will still have 1 more candy. If Lenka give Alena 1 candy Alena will hame twice more than Lenka. How many candies have each of them?
17. Three friends Three friends divided the profit 104,650 CZK, so that for every 4 CZK, which got the first friend equals 5 crowns for second and for every 9 CZK, which got the second equals 16 CZK for third. Question: Who got the most and how much.
18. Sum 10 What is the probability that two dice throw twice in a row will result the sum of 10?
19. Water tank The water tank has a cylindrical shape with a base diameter of 4.2 m and is 80 cm deep. How many minutes will take fill it 10 cm below the edge of the tank if water flowing 2 liters per second?
20. Costume Denisa is preparing for a goldsmith's costume carnival. During the preparations, she thought she would let her hair wipe instead - she would apply a 5 μm thick layer of gold to each hair. How much gold would Denisa need? Assume that all hundred thousand De

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