# Examples for 9th grade - page 57

1. Triangle - is RT? Triangle has a circumference of 90 cm. Side b is 1 cm longer than c, side c is 31 cm longer than side a. Calculate the length of sides and determine whether triangle is a right triangle.
2. Surface area of cylinder Determine the lateral surface of the rotary cylinder which is circumscribed cube with edge length 5 cm.
3. Outer angles The outer angle of the triangle ABC at the A vertex is 71°40 ' outer angle at the vertx B is 136°50'. What size has the inner triangle angle at the vertex C?
4. Salt 1 t of sea water contains 25 kg of salt. How many tons of seawater must be evaporated to obtain 2 q of salt? On a weekly forest brigade operates 12 students. After plant one hundred spruces get x CZK, anfter one hundred pines y CZK. How many CZK got one student for one day if planted spruces 25000 and 30000 pines week?
6. Prism bases Volume perpendicular quadrilateral prism is 360 cm3. The edges of the base and height of the prism are in the ratio 5:4:2 Determine the area of the base and walls of the prism.
7. Mason with assistant Mason had to complete the work in 10 days. Two and a half days later his assistant arrived. Together they completed the work in next three and a half days. How many days would he need an assistant for the same work?
8. Float boya A 0.5 meter spherical float is used as a location mark for a fishing boat anchor. It floats in salt water. Find the depth to which the float sinks if the material of which the float is made weighs 8 kilograms per cubic meter and salt water weighs 1027 kg/m
9. Work at plant Handyman has vowed to do repair work at the plant for 25 days. However, work had to be shortened and therefore gained helper. Together they made all the corrections for 13 1/3 days. How long the work would take helper himself?
10. Four classses Students of all 7, 8 and 9 classes in one school may take up 4,5,6 and 7 abreast and nobody will left. How many is the average count of pupils in one class if there are always four classes each grade?
11. Sisters Sisters Janka and Danka are saved together 220 CZK. On a trip to Janka wants to take a fifth of her savings and Danka quarter. Then they will have 50 CZK on the trip. How much money saved Janka and Danka?
12. Percentage reduction Reducing the unknown number by 19% get number 700.7 Determine unknown number.
13. Trapezium The length of the base and the height size of the base of the trapezium is at ratio 5:3:2, the content area of the trapezium is 128 cm2. Calculate the length of the base and the height of the trapezoid.
14. Diagonals Draw a square ABCD whose diagonals have a length of 6 cm
15. Isosceles trapezoid In an isosceles trapezoid KLMN intersection of the diagonals is marked by the letter S. Calculate the area of trapezoid if /KS/: /SM/ = 2:1 and a triangle KSN is 14 cm2.
16. Resort In a completely crowded resort was 30% from the Czech Republic quarter visitors were from Slovakia and the rest 135 came from Germany. What capacity have resort?
17. Plan scale At what scale is drawn plan of the building, where one side of the building is 45 meters long is on the plan expressed by a straight line 12 mm long.
18. Is right? Determine whether the triangle with legs (catheti) 19.5 cm and 26 cm and length of the hypotenuse 32.5 cm is rectangular?
19. Triangle midpoints Determine coordinates of triangle ABC vertices if we know tirangle sides midpoints SAB [0;3] SBC [1;6] SAC [4;5], its sides AB, BC, AC.
20. Prism Calculate the height of the prism having a surface area 448.88 dm² wherein the base is square with a side of 6.2 dm. What will be its volume in hectoliters?

Do you have an interesting mathematical word problem 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 the e-mail correctly and check whether you don't have a full mailbox.

Please do not submit problems from current active competitions such as Mathematical Olympiad, correspondence seminars etc...