# Examples for 9th grade - page 28

1. Cross-country competition
Cross-country competition was attended by 76% of pupils of class 9.B. Class consis of 16 boys, two of whom did not run and 4 girls did not run. How many girls go to class 9.B?
2. Roller
Roller has a diameter of 0.96 m and a width 169 cm. How many m2 of road level when he turns 42-times?
3. Racing track
On the racing track circling three cars. The first passes one circuit for 8 seconds, the second for 20 seconds and a third for 8 seconds. a) Calculate number of seconds since the start to catch all three cars together for the first time again across the s
4. Aircraft
The aircraft has in a fuel tank 68 hl of aviation fuel and flight consumes 3.6 liters of fuel. Identify the function, which expresses the dependence of the volume of fuel in tank on the track distance plane flew by. How many hectolites of fuel is still in
5. RT 11
Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
6. Journey
The road from A to B measures 11.5 km. Firstly up the hill, then by level plane and then downhill. Tourist goes uphill at 3 km/h, on the plane 4 km/h and downhill 5 km/h. From point A to B went 2h 54 min back 3h 6 min. How long is the segment of level pla
7. Quadrangular prism
The quadrangular prism has a volume 648 cm3. Trapezoid which is its base has the dimensions bases: a = 10 cm, c = 5 and height v = 6 cm. What is the height of the prism?
8. Combi-triangle
On each side of the square is marked 10 different points outside the vertices of the square. How many triangles can be constructed from this set of points, where each vertex of the triangle lie on the other side of the square?
9. Gauss
Help little C.F. Gauss sum all the integers from 1 to 400.
10. Two typists
There are two typists who are rewriting the material 814 pages. First can it handle rewrite yourself for 24 days; the second 12 days. First typist wrote material yourself 4 days rest rewrites yourself second typist. How many days will it take rewriting alt
11. IS trapezoid
Isosceles trapezoid arm measured 35 cm. Height is 30 cm and middle segment is 65 cm. Determine length of its bases.
12. Diamond ABCD
In the diamond ABCD is the diagonal e = 24 cm and size of angle SAB is 28 degrees, where S is the intersection of the diagonals. Calculate the circumference of the diamond.
13. Estate
Estate shaped rectangular trapezoid has bases long 34 m , 63 m and perpendicular arm 37 m. Calculate how long is its fence.
14. Angles in triangle
The triangle is ratio of the angles β:γ = 6:8. Angle α is 40° greater than β. What are the size of angles of the triangle?
15. Ice cream in cone
In the ice cream cone with a diameter of 5.2 cm is 1.3 dl of ice cream. Calculate the depth of the cone.
16. Carpenter
From wooden block carpenter cut off a small cuboid block with half the edge length. How many percent of wood he cut off?
17. 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.
18. Square pyramid
Calculate the volume of the pyramid with the side 5cm long and with a square base, side-base has angle of 60 degrees.
19. Euclid theorems
Calculate the sides of a right triangle if leg a = 6 cm and a section of the hypotenuse, which is located adjacent the second leg b is 5cm.
20. 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.

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