# Examples for 9th grade - page 23

- Truck

In 7 hours started from town Krnov truck at speed 40 km/h. Passenger car started against it in 8 hours 30 minutes from the city of Jihlava at speed 70 km/h. Distance between this two cities is 225 km. At what time and at what distance from Krnov this two. - Triangular pyramid

It is given perpendicular regular triangular pyramid: base side a = 5 cm, height v = 8 cm, volume V = 28.8 cm^{3}. What is it content (surface area)? - Pharmacy

At the pharmacy are in one container 20% solution in the second 50% solution of disinfectant. They need to prepare 4 L of 48-percent solution. What amount of solution from each container is needed to mix? - Circle

On the circle k with diameter |MN| = 61 J lies point J. Line |MJ|=22. Calculate the length of a segment JN. - Volume from surface area

What is the volume of the cube whose surface area is 96 cm^{2}? - Salary

Lawyer got to pay 840 Euros in banknotes of 20 and 50 Eur. Total got 18 banknotes. How many was which? - Rectangle - desc circle

Length of the sides of the rectangle are at a ratio 1: 3 . Radius of the circle circumscribed to rectangle is 10 cm. Calculate the rectangle's perimeter. - Hexagonal pyramid

Base of the pyramid is a regular hexagon, which can be circumscribed in a circle with a radius of 1 meter. Calculate the volume of a pyramid 2.5 meters high. - Numbers

How many different 7 digit natural numbers in which no digit is repeated, can be composed from digits 0,1,2,3,4,5,6? - Cubes

Surfaces of cubes, one of which has an edge of 48 cm shorter than the other, differ by 36288 dm^{2}. Determine the length of the edges of this cubes. - Area codes

How many 6 digit area codes are possible if the first number can't be zero? - Diagonals

Rhombus has two diagonals e=14 dm and f=11 dm. Calculate the side angle and height of the rhombus. - Circles

Three circles of radius 95 cm 78 cm and 64 cm is mutually tangent. What is the perimeter of the triangle whose vertices are centers of the circles? - Tributaries

The first tributary fill pool with water in 15 hours. The second tributary fill pool in 10 hours. For how many hours the pool is filled with both tributaries? - Three drivers

Three driversdriving the same direction found that they have same amounth of gasoline. The first is enough to go 6 km, 4 km second and third 3km. Gasoline they divided so all three just drove to the nearest petrol station. How many km away was a petrol sta - Four pupils

Four pupils divided $ 1485 so that the second received 50% less than the first, the third 1/2 less than a fourth and fourth $ 154 less than the first. How much money had each of them? - Angles in a triangle

The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=83°. What sizes have other angles in a triangle? - Hexagon 5

The distance of parallel sides of regular hexagonal is 61 cm. Calculate the length of the radius of the circle described to this hexagon. - Park

In the newly built park will be permanently placed a rotating sprayer irrigation of lawns. Determine the largest radius of the circle which can irrigate by sprayer P so not to spray park visitors on line AB. Distance AB = 55 m, AP = 36 m and BP = 28 m. - Semicircle

In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?

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