# Examples for 8th grade - page 26

1. Rope
One half of rope use Mam for packaging, half of the rest got son, half of the rest he took father and two fifths of what remained, got daughter. Remained 143 cm of rope. How long was rope at the beginning?
2. OPT
What is the perimerer of a right triangle with the cathetuses 16 cm and 14 cm?
3. 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.
4. 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.
5. Machines
In the workshop are three machines. The first is treated 250 parts for 4.7 hours, the second is treated 300 parts for 1.9 hours and the third is treated 230 parts for 4.6 hours. How long will take to make 3100 parts if worked all three machines at the.
6. Semicircle
In the semicircle with center S and the diameter AB is constructed equilateral triangle SBC. What is the magnitude of the angle ∠SAC?
7. 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.
8. 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.
9. 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?
10. 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?
11. 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?
12. Rail turn
The curve radius on the railway line is 532 m . Length of rail track on it is 818 m. How many degrees is the angle ASB, if A and B are boundary points and S is center of arc curve.
13. 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?
14. 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
15. Sun rays
If the sun's rays are at an angle 60° then famous Great Pyramid of Egypt (which is now high 137.3 meters) has 79.3 m long shadow. Calculate current height of neighboring chefren pyramid whose shadow is measured at the same time 78.8 m and the current hei
16. Series
Andrew wrote this series of numbers: 1,3,7,15, .... n. Which number in the series does not belong? ?
17. Ladislav in Amsterdam
Ladislav was reward and went to conference in Amsterdam. Conferense fee was € 3484. Calculate how many books Ladislav could buy at the price of 48 and 52 euros if he don't want fill whole home library and he can buy only 70 books?
18. Fixed expenses 2013
Since 2013, the Slovak government plans to tax more small one person businesses. Instead of fixed expences 40% will be fixed expences 40% of gross income up to 420 Eur. Calculate what percentage of fixed expences will in 2013 pays from gross income 1569 E
19. Vertical prism
The base of vertical prism is a right triangle with leg a = 5 cm and a hypotenuse c = 13 cm. The height of the prism is equal to the circumference of the base. Calculate the surface area and volume of the prism
20. Common chord
Two circles with radius 17 cm and 20 cm are intersect at two points. Its common chord is long 27 cm. What is the distance of the centers of these circles?

Do you have an interesting mathematical example that you can't solve it? Enter it, and we can try to solve it.

To this e-mail address, we will reply solution; solved examples are also published here. Please enter e-mail correctly and check whether you don't have a full mailbox.