# Examples for 9th grade - page 13

- Pentagon

Within a regular pentagon ABCDE point P is such that the triangle is equilateral ABP. How big is the angle BCP? Make a sketch. - Estate

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

How many rectangles with area 3032 cm^{2}whose sides is natural numbers are? - 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? - Stairway

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

Road has climbing 1:27. How big is a angle corresponds to this climbing? - Square 2

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

How many times must throw the dice, the probability of throwing at least one six was greater than 90%? - Square grid

Square grid consists of a square with sides of length 1 cm. Draw in it at least three different patterns such that each had a content of 6 cm^{2}and circumference 12 cm and that their sides is in square grid. - 4s pyramid

Regular tetrahedral pyramid has a base edge a=17 and collaterally edge length b=32. What is its height? - Triangular pyramid

Calculate the volume and surface area of a regular triangular pyramid whose height is equal to the length of the base edges 10 cm. - Football league

In the 5th football league is 10 teams. How many ways can be filled first, second and third place? - 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. - Circle section

Equilateral triangle with side 33 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. - The chord

Side of the triangle inscribed in a circle is a chord passing through circle center. What size are the internal angles of a triangle, if one of them is 40°? - Cut and cone

Calculate the volume of the rotation cone which lateral surface is circle arc with radius 15 cm and central angle 63 degrees.

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