# Examples for 9th grade - page 25

- Diagonals

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

What is the average speed of the car, where half of the distance covered passed at speed 66 km/h and the other half at 86 km/h. - Four pupils

Four pupils divided $ 1805 so that the second received 40% less than the first, the third 1/2 less than a fourth and fourth $ 78 less than the first. How much money had each of them? - 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. - Area codes

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

After we cycle five hockey players sit down. What is the probability that the two best scorers of this crew will sit next to each other? - Baker

The baker makes from 10 kg of flour 12 kg dough. How much flour he need to make a 100 kg dough? - Angles in a triangle

The angles of the triangle ABC make an arithmetic sequence with the largest angle γ=60°. What sizes have other angles in a triangle? - Semicircle

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

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

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