# Examples for 9th grade - page 13

- 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 34 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. - 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. - Jewel

Rhombus-shaped jewel have area of 153 mm^{2}and the edge in long 13.9 mm. Calculate the size of rhombus acute angle. - 4s pyramid

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

Are diagonals in a rectangular trapezoid perpendicular and bisect the angles? - Circle and angle

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

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

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

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

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

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

Calculate the circumference and area of the rhomboid with sides 20 and 10, with their angle 20°. - Steeple

Steeple seen from the road at an angle of 75°. When we zoom out to 25 meters, it is seen at an angle of 20°. What is high?

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