# Examples for 9th grade - page 12

- Trains

From station 130 km away started passenger train and after 2.2 hours after the express train, which travels 37 km an hour more. Express train finish journey 7 minutes early. Calculate the average speed of this two trains. - Octahedron - sum

On each wall of a regular octahedron is written one of the numbers 1, 2, 3, 4, 5, 6, 7 and 8, wherein on different sides are different numbers. For each wall John make the sum of the numbers written of three adjacent walls. Thus got eight sums, which also. - Wire

One pull of wire is reduced its diameter by 14%. What will be diameter of wire with diameter 19 mm over 10 pulls? - n-gon II

What is the side length of the regular 5-gon circumscribed circle of radius 11 cm? - Estate

Semicircle estate must be fence. The straight section has 26 meters long fence. How many meters of fence should buy? - 4side pyramid

Calculate the volume and surface of 4 side regular pyramid whose base edge is 4 cm long. The angle from the plane of the side wall and base plane is 60 degrees. - OK circle

Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 33 and one cathetus long 17. - Canopy

Mr Peter has metal roof cone shape with a height of 101 cm and radius 189 cm over well. He needs paint the roof with anticorrosion. How many kg of color must he buy if the manufacturer specifies the consumption of 1 kg to 4.3 m^{2}? - Stairway

What angle rising stairway if step height in 17 cm and width 27 cm? - Square 2

Points D[10,-8] and B[4,5] are opposed vertices of the square ABCD. Calculate area of the square ABCD. - Prism

Calculate the volume of the rhombic prism. Base of prism is rhombus whose one diagonal is 47 cm and the edge of the base is 28 cm. The edge length of the base of the prism and height is 3:5. - Pyramid a+h

Calculate the volume and surface area of the pyramid on the edge and height a = 26 cm. h = 3 dm. - Climb

Road has climbing 1:27. How big is a angle corresponds to this climbing? - n-gon

Gabo draw n-gon, which angles are consecutive members of an arithmetic sequence. The smallest angle is 70° biggest 170°. How many sides have Gabo's n-gon? - Two doctors

Doctor A will determine the correct diagnosis with a probability 92% and doctor B with a probability 88%. Calculate probability of correct diagnosis if patient is diagnosed by both doctors. - Rectangles

How many rectangles with area 3002 cm^{2}whose sides is natural numbers are? - Motion

From two different locations distant 232 km started against car and bus. The car started at 5:20 with average speed 64 km/h. Bus started at 7:30 with average speed 80 km/h. When they meet? How many kilometers went the bus? - Rotary cone

Rotary cone whose height is equal to the circumference of the base, has a volume 229 cm^{3.}Calculate the radius of the base circle and height of the cone. - Sale

If the product twice price cut by 25%, what percentage was price cut in total? - 2x cone

Circular cone height 76 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone.

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