# Examples for 9th grade - page 7

- Seating

How many ways can 7 people sit on 3 numbered chairs (eg seat reservation on the train)? - IS triangle

Calculate interior angles of the isosceles triangle with base 38 cm and legs 26 cm long. - 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. - 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. - Prism

Right angle prism, whose base is right triangle with leg a = 7 cm and hypotenuse c = 15 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 - 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. - Percentages above 100%

What is 122% of 185? What is the meaning of percentages above 100%? - 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 - Cone

Calculate volume and surface area of the cone with diameter of the base d = 15 cm and side of cone with the base has angle 52°. - Slope of track

Calculate the average slope (in promiles and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Topoľčany (174 m AMSL), if the track is 44 km long. - 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? - Railways

Railways climb 7.4 ‰. Calculate the height difference between two points on the railway distant 3539 meters. - 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? - Pentagon

Calculate the area of regular pentagon, which diagonal is u=17. - Right triangle

Legs of right are in ratio a:b = 6:8. Hypotenuse has a length of 61 cm. Calculate the perimeter and area of the triangle. - Mast

Mast has 13 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 15°. Determine the height of the mast, if the sun above the horizon is at angle 33°. - Rhombus

It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a_{1}= 14 cm and a_{2}= 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus. - Sea water

Seawater contains about 4.3% salt. How many dm^{3}of distilled water we must pour into 5 dm^{3}of sea water to get water with 1.8% salt? - Road repair

Road repair took 10 days for 36 workers if they worked 9 hours a day. How many days take repair same road 37 workers if they work 8 per day?

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