# Examples for 9th grade - page 25

- 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. - 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)? - Area codes

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

The base of prism is a rectangle with a side of 7.5 cm and 12.5 cm diagonal. The volume of the prism is V = 0.9 dm^{3}. Calculate the surface of the prism. - Rhombus

Calculate the length of the diagonal AC of the rhombus ABCD, if its perimeter is 84 dm and the other diagonal BD has length 20 dm. - Semicircle

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

Cylindrical tank were poured with 3.5 liters of water. If tank base diameter is 3 dm, how height is water level in? - 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? - Cone

If the segment of the line y = -3x +4 that lies in quadrant I is rotated about the y-axis, a cone is formed. What is the volume of the cone? - Above Earth

To what height must a boy be raised above the earth in order to see one-fifth of its surface. - The cone

The lateral surface area of the cone is 4 cm^{2}, the area of the base of the cone is 2 cm^{2}. Determine the angle in degrees (deviation) of the cone sine and the cone base plane. (Cone side is the segment joining the vertex cone with any point of the base ci - Hairs

Suppose the length of the hair is affected by only the α-keratin synthesis, which is the major component. This synthesis takes place in the epithelial cells of the hair bulb. The structure of α-keratin is made up of α-helix, wherein in one revolution it is - Two valves

Water fill the pool by two valves for 11 days. After 7 days the first valve was stopped and the second valve fill pool for 7 days. How many days took to fill the pool each of the valves individually? - Toys

3 children pulled 12 different toys from a box. Many ways can be divided toys so that each children had at least one toy?

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