# Examples for secondary school students - page 23

1. Volume and surface Calculate the volume and surface area of the cylinder when the cylinder height and base diameter is in a ratio of 3:4 and the area of the cylinder jacket is 24 dm2.
2. Trapezoid - hard example Base of the trapezoid are: 24, 16 cm. Diagonal 22, 26 cm. Calculate its area and perimeter.
3. Reciprocal What is the reciprocal of the sum of the reciprocals of 4 and 9?
4. Moon We see Moon in the perspective angle 28'. Moon's radius is 1740 km at the time of the full moon. Calculate the mean distance of the Moon from the Earth.
5. Internal angles The ABCD is an isosceles trapezoid, which holds: |AB| = 2 |BC| = 2 |CD| = 2 |DA|: On its side BC is a K point such that |BK| = 2 |KC|, on its side CD is the point L such that |CL| = 2 |LD|, and on its side DA the point M is such that | DM | = 2 |MA|. Dete
6. JUDr. Usury Judge JUDr. Usury approved the agreement on guilt and punishment where confessed to pay daily interest 0.18%. How big is a yearly interest? Year has 360 days.
7. Tourist Jirka Distance between the points A and B is 13.5 km. Jirka went from point A to point B unknown speed and for an unknown period of time. Back to the point A went slower by 3 km/h which means that went 20 minutes more. How long Jirka took the return journey?
8. Bomber Bomber flies 10 km at 600 km/h. At what horizontal distance from the target, must pilot drop the bomb to hit the target? Don't care about air resistance and consider the gravitational acceleration g=9.81 m/s2.
9. Population The town has 65,000 inhabitants. 40 years ago there were 157,000. How many people will live in town in 10 years if the average rate in population is as in previous years? Grandson with grandpa they counted how many years have together. Their product is 365. How many years is the sum of their years. Solve quadratic equation: 2x2-58x+396=0
12. Two cars From the town A to town B started two cars. The first at 7:00 at average speed 60 km per hour, the second at 10:00 at average speed 100 km per hour. The first car will not stay in B, and on the way back meet the second car at half way from A to B. At what.
13. Future of libraries You know that thanks to the Internet, electronic communications and developing online resources on the Internet annually declining number of traditional readership by 17%. These deal is irreversible evolutionary shift from old books from libraries to immed
14. Square If the length of the sides of the square we decrease by 25% decrease the content area of 28 cm2. Determine the side length of the original square.
15. Surface of the cylinder Calculate the surface area of the cylinder when its volume is 45 l and the perimeter of base is three times of the height.
16. Circle sector Circular sector with a central angle 80 ° has area 1257 cm2. Calculate its radius r.
17. Building The building I focused at an angle 30°. When I moved 5 m building I focused at an angle 45°. What is the height of the building?
18. Cars plates How many different licence plates can country have, given that they use 3 letters followed by 3 digits?
19. Four-digit number Find also a four-digit number, which quadrupled written backwards is the same number.
20. Workman - shift The worker produces 300 components per shift. How many components would be produced in 18 shift, if his performance gradually increased every shift by 3 components?

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