# Examples for 9th grade - page 6

1. Triangle ABC Calculate the sides of triangle ABC with area 1404 cm2 and if a: b: c = 12:7:18
2. 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 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?
4. IS triangle Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long.
5. IS trapezoid Calculate the length of diagonal u and height v of isosceles trapezoid ABCD, whose bases have lengths a = |AB| = 37 cm, c = |CD| = 29 cm and legs b = d = |BC| = |AD| = 28 cm.
6. 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.
7. Prism Right angle prism, whose base is right triangle with leg a = 3 cm and hypotenuse c = 13 cm has same volume as a cube with an edge length of 3 dm. a) Determine the height of the prism b) Calculate the surface of the prism c) What percentage of the cube
8. 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.
9. Cone Calculate volume and surface area of ​​the cone with a diameter of the base d = 15 cm and side of cone with the base has angle 52°.
10. Steps How many steps you save if you go square estate for diagonal (crosswise), rather than circumvent on the two sides of its perimeter with 307 steps.
11. Railways Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters.
12. Percentages above 100% What is 122% of 185? What is the meaning of percentages above 100%?
13. Z9–I–1 In all nine fields of given shape to be filled natural numbers so that: • each of the numbers 2, 4, 6 and 8 is used at least once, • four of the inner square boxes containing the products of the numbers of adjacent cells of the outer square, • in the cir
14. Slope of track Calculate the average slope (in permille and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitrianske Pravno (354 m AMSL), if the track is 11 km long.
15. Climb in percentage The height difference between points A and B is 475 m. Calculate the percentage of route climbing if the horizontal distance places A, B is 7.4 km.
16. Cyclist Cyclist goes uphill 10 km for 50 minutes and downhill minutes for 29 minutes, both applied to the pedals same force. How long he pass 10 km by plane?
17. Right triangle Legs of the right triangle are in the ratio a:b = 2:8. The hypotenuse has a length of 87 cm. Calculate the perimeter and area of the triangle.
18. Spherical cap From the sphere of radius 18 was truncated spherical cap. Its height is 12. What part of the volume is spherical cap from whole sphere?
19. Pentagon Calculate the area of regular pentagon, which diagonal is u=17.
20. Rhombus It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.

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