# Examples for 9th grade - page 12

- 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. - Trains

From station 130 km away started passenger train and after 2.8 hours after the express train, which travels 24 km an hour more. Express train finish journey 14 minutes early. Calculate the average speed of this two trains. - Rectangles

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

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

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

Circular cone with height h = 11 dm and base radius r = 4 dm slice plane parallel to the base. Calculate distance of the cone vertex from this plane, if solids have the same volume. - 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. - Sequence

In the arithmetic sequence is a_{1}=-9, d=4. Which member is equal to the number 147? - Balls

Ping pong balls have a diameter of approximately 3 cm. They are sold in boxes of 3 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 wit - Pillar

Calculate volume of pillar shape of a regular tetrahedral truncated pyramid, if his square have sides a = 13, b = 21 and height is h = 33. - Dice

How many times must throw the dice, the probability of throwing at least one three was greater than 90%? - Pyramid a+h

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

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

Rafael works for the Slovak railways since 1987. His salary is 874 €. His colleague, Asterios works in the Greek State Railways from 2001. Earns 5670 € per month. Calculate how many times earns Asterios more than Asterios? - Cylinder - A&V

The cylinder has a volume 253. The base has a radius 5. What is the area of surface of the cylinder? - Rhomboid

Calculate the circumference and area of the rhomboid with sides 11 and 17, with their angle 70°. - Football league

In the 2nd football league is 19 teams. How many ways can be filled first, second and third place? - Moving

Vojta left the house at three o'clockat 4 km/h. After half hour later went from the same place Filip by bicycle at speed 25 km/h. How long take Tilip to catch up Vojta and how far from the house? - Posters

Column with posters in the form of a cylinder is 3.3 m high and its diameter is 1.5 m. What is the content area for which it is possible to stick posters?

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