# Examples for secondary school students - page 4

- Pipes

Water pipe has a cross-section 1405 cm^{2}. An hour has passed 756 m^{3}of water. How much water flows through the pipe with cross-section 300 cm^{2}per 15 hours if water flow same speed? - Circles

The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle. - Two cars

Two cars started against each other at the same time to journey long 293 km. First car went 41 km/h and second 41 km/h. What distance will be between this cars 20 minutes before meet? - Forces

In point O acts three orthogonal forces: F_{1}= 20 N, F_{2}= 7 N and F_{3}= 19 N. Determine the resultant of F and the angles between F and forces F_{1}, F_{2}and F_{3}. - Cylinders

Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much? - Ace

From complete sets of playing cards (32 cards) we pulled out one card. What is the probability of pulling the ace? - Flags

How many different flags can be made from colors purple, yellow, red, white, blue, green, orange so that each flag consisted of three different colors? - Circle arc

Circle segment has a circumference of 41.89 m and 251.33 m^{2}area. Calculate the radius of the circle and size of central angle. - Numbers

Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum? - Vans

In how many ways can 7 shuttle vans line up at the airport? - Right

Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ? - Triangle ABC

Calculate the sides of triangle ABC with area 1404 cm^{2}and if a: b: c = 12:7:18 - Crystal

Crystal grows every month 1.9 promile of its mass. For how many months to grow a crystal from weight 360 g to 593 g? - Triangle

Triangle KLM is given by plane coordinates of vertices: K[-12, -11] L[-15, -18] M[-13, -12]. Calculate its area and itsinterior angles. - Ravens

The tale of the Seven Ravens were seven brothers, each of whom was born exactly 2.5 years after the previous one. When the eldest of the brothers was 2-times older than the youngest, mother all curse. How old was seven ravens brothers when their mother cur - Tractors

Fields go plow two tractors with various performance. The first tractor plow whole field in 11 hours, the second tractor plow whole field 19 hours longer. How long take plow whole field with two tractors? - Meadow

On the meadow grazing horses, cows and sheep, together less than 200. If cows were 45 times more, horses 60 times more and sheep 35 times more than there are now, their numbers would equall. How many horses, cows and sheep are on the meadow together? - Seating

How many ways can 9 people sit on 3 numbered chairs (eg seat reservation on the train)? - Gutter

How much metal is needed for production 46 pieces of gutter pipes with the diameter 12 cm and length of 4 m? The plate bends add 2% of the material. - Cuboid diagonal

Calculate the volume and surface area of the cuboid ABCDEFGH, which sides abc has dimensions in the ratio of 9:3:8 and if you know that the wall diagonal AC is 86 cm and angle between AC and the body diagonal AG is 25 degrees.

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