# Examples for 9th grade - page 28

1. 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
2. RT 11 Calculate the area of right tirangle if its perimeter is p = 45 m and one cathethus is 20 m long.
3. 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?
4. Gauss Help little C.F. Gauss sum all the integers from 1 to 400.
5. 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
6. 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.
7. IS trapezoid Isosceles trapezoid arm measured 35 cm. Height is 30 cm and middle segment is 65 cm. Determine length of its bases.
8. 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.
9. Estate Estate shaped rectangular trapezoid has bases long 34 m , 63 m and perpendicular arm 37 m. Calculate how long is its fence.
10. 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?
11. 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.
12. 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.
13. 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.
14. Carpenter From wooden block carpenter cut off a small cuboid block with half the edge length. How many percent of wood he cut off?
15. Reciprocal What is the reciprocal of the sum of the reciprocals of 4 and 9?
16. Mountain railway Height difference between points A, B of railway line is 38.5 meters, their horizontal distance is 3.5 km. Determine average climb in permille up the track.
17. 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.
18. Car The driver of a car is to get to 608 km distant city. From atlas found that 162 km will have to pass through the cities at average speed 48 km/h. Remainder of the journey pass outside the cities at average speed 116 km/h. Calculate how many hours it will t
19. Two diggers There are two diggers. One digger digs a pit 46 hours second gidding 2 times faster. a) how long took to dig a pit second digger b) how long took dig together
20. Sphere cuts At what distance from the center intersects sphere with radius R = 56 plane, if the cut area and area of the main sphere circle is in ratio 1/2.

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