# Examples for 9th grade - page 25

1. 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.
2. 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.
3. 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?
4. 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?
5. Above Earth
To what height must a boy be raised above the earth in order to see one-fifth of its surface.
6. 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?
7. 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?
8. 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
9. 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
10. 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
11. Series
Andrew wrote this series of numbers: 1,3,7,15, .... n. Which number in the series does not belong? ?
12. 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?
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?
14. 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
15. 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
16. Mushrooms
Fresh mushrooms contain 94% water, dried 14%. How many kg of fresh mushrooms is needed to collect to get 10 kg dried?
17. Rhombus diagonal
Area of rhombus is 224. One diagonal measures 33, find length of other diagonal.
18. Line
Line p passing through A[-10, 6] and has direction vector v=(3, 2). Is point B[7, 30] on the line p?
19. Leg
Determine the area of a trapezoid with bases 71 and 42 and height is 4 shorter than the its leg.
20. Loan
Apply for a \$ 59000 loan, the loan repayment period is 8 years, the interest rate 7%. How much should I pay for every month (or every year if paid yearly). Example is for practise geometric progression and/or periodic payment for an annuity.

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.