# Examples for 9th grade - page 12

- 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. - Climb

Road has climbing 1:23. 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? - OK circle

Calculate the radius (circumradius) of the circle described right triangle with hypotenuse long 43 and one cathetus long 21. - Motion

From two different locations distant 104 km started against car and bus. The car started at 5:30 with average speed 58 km/h. Bus started at 6:40 with average speed 79 km/h. When they meet? How many kilometers went the bus? - Pyramid a+h

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

Rotary cone whose height is equal to the circumference of the base, has a volume 4772 cm^{3.}Calculate the radius of the base circle and height of the cone. - Rectangles

How many rectangles with area 2832 cm^{2}whose sides is natural numbers are? - Two doctors

Doctor A will determine the correct diagnosis with a probability 80% and doctor B with a probability 72%. Calculate probability of correct diagnosis if patient is diagnosed by both doctors. - 2x cone

Circular cone height 60 cm was cut plane parallel with base. Volume of these two small cones is the same. Calculate the height of the smaller cone. - Cut and cone

Calculate the volume of the rotation cone which lateral surface is circle arc with radius 14 cm and central angle 114 degrees. - Circle section

Equilateral triangle with side 50 is inscribed circle section whose center is in one of the vertices of the triangle and the arc touches the opposite side. Calculate: a) the length of the arc b) the ratio betewwn the circumference to the circle sector. - Sale

If the product twice price cut by 20%, what percentage was price cut in total? - Jewel

Rhombus-shaped jewel have area of 86 mm^{2}and the edge in long 10 mm. Calculate the size of rhombus acute angle. - 4s pyramid

Regular tetrahedral pyramid has a base edge a=6 and collaterally edge length b=15. What is its height? - Circle and angle

What is the length of the arc of a circle with radius r = 138 cm with cental angle 2.07 rad? - Accidents

The count of accidents in 1993 caused 8009 women which is 7.1%. How many men caused the accidents? - Trapezoid

Are diagonals in a rectangular trapezoid perpendicular and bisect the angles? - Tetrahedral pyramid

Calculate the volume and surface of the regular tetrahedral pyramid if content area of the base is 20 cm^{2}and deviation angle of the side edges from the plane of the base is 60 degrees. - RT - hypotenuse and altitude

Right triangle TWS has hypotenuse s=202 km and altitude to s is 99 km. How long are hypotenuse segments?

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