# Examples for 9th grade - page 14

- 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. - 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. - 4s pyramid

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

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

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

Rhombus-shaped jewel have area of 93 mm^{2}and the edge in long 13.2 mm. Calculate the size of rhombus acute angle. - 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. - 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°? - Trapezoid

Are diagonals in a rectangular trapezoid perpendicular and bisect the angles? - 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. - Sequence

In the arithmetic sequence is a_{1}=-1, d=4. Which member is equal to the number 203? - RT - hypotenuse and altitude

Right triangle BTG has hypotenuse g=117 m and altitude to g is 54 m. How long are hypotenuse segments? - Circle and angle

What is the length of the arc of a circle with radius r = 207 mm with cental angle 5.33 rad? - Pillar

Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 19, b = 27 and height is h = 48. - Stock market

Simon one day decided to invest € 62000 to the stock market. After six months he invested July 25 stock markets fell by 47%. Fortunately for Simon from July 25 5 to October 25 his shares have risen by 39%. Simon is then: ? - Painter Pavel

Painter Pavel painted the fence for 16 hours and painter Petr the same fence painted for 13 h. How long should take painted the fence together? - Discounts on rail (ZSSK)

The railway company ZSSK offers a discount of 15% (REGIONAL) for 5 Eur/year. Calculate the real discount rate as a percentage, where passengers will travel 19 Eur per week. - Balls

Ping pong balls have a diameter of approximately 4.6 cm. They are sold in boxes of 4 pieces: each box has the shape of a cuboid with a square base. The balls touch the walls of the box. Calculate what portion of the internal volume of the box is filled w - Accidents

The count of accidents in 1995 caused 8780 women which is 8.4%. How many men caused the accidents?

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