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 cm3. 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.
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 dm3. Calculate the surface of the prism.
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.
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?
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?
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 cm2, the area of the base of the cone is 2 cm2. 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
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?
3 children pulled 12 different toys from a box. Many ways can be divided toys so that each children had at least one toy?