# Examples for 9th grade - page 36

1. Tin with oil Tin with oil has the shape of a rotating cylinder whose height is equal to the diameter of its base. Canned surface is 1884 cm2. Calculate how many liters of oil is in the tin.
2. Sports games Pupils of same school participated district sports games. When dividing into teams found that in the case of the creation teams with 4 pupils remaining 1 pupil, in the case of a five-member teams remaining 2 pupils and in the case of six-members teams r
3. Cable car Cable car rises at an angle 45° and connects the upper and lower station with an altitude difference of 744 m. How long is "endless" tow rope?
4. Car rent Rental cars are paid a fixed daily fee plus 16 cents for each kilometer traveled. Samuel want to rent a car for a day and worked out that will pay 175 euros. When paying he got a 20% discount on the daily fee, the cost per kilometer is unchanged. Samuel th
5. Rhombus IV Calculate the length of the diagonals of the rhombus, whose lengths are in the ratio 1: 2 and a rhombus side is 35 cm.
6. Father and son Father is 48 years old, son 23. When will be the father twice older than a son?
7. Logs The log has diameter 30 cm. What's largest beam with a rectangular cross-section can carve from it?
8. Rotary cylinder The rotating cylinder has a surface area 69.08 cm2. The area of the shell is 62.8 cm 2. What is the diameter of the cylinder?
9. Bus stop Determine at what time the bus leaves from the bus stop outside the village, if you know that when you leave home at 8:00 and go at speed 3 km/h, you come to a stop 9 minutes after the departure of the bus, and when you go speed at 4 km/h, you come to the
10. Chord - TS The radius of circle k measures 68 cm. Arc GH = 47 cm. What is TS?
11. Angles and sides of the triangle Triangle ABC has a circumference of 26 cm. Lengths of the sides are as follows: a = 11.2 cm; b = 6.5 cm. Arrange the interior angles in order of its size. ?
12. Diagonal in rectangle In that rectangle ABCD is the center of BC point E and point F is center of CD. Prove that the lines AE and AF divide diagonal BD into three equal parts.
13. The hall The hall had a rectangular ground plan one dimension 20 m longer than the other. After rebuilding the length of the hall declined by 5 m and the width has increased by 10 m. Floor area increased by 300 m2. What were the original dimensions of the hall?
14. Copiers The new copier copying a folder of papers 5 min. faster than the old. The operator used new, but out of toner and exchange took 5 min. In that time copied on the old. The whole work has been done for 9 min. How long would the work done only by old copier?
15. Rectangle - sides What is the perimeter of a rectangle with area 266 cm2 if length of the shorter side is 5 cm shorter than the length of the longer side?
16. Alloy The first alloy is a mixture of two metals in the ratio 1:2, the second is a mixture of same metals in the ratio 2:3. At what ratio we have these two alloys put into the furnace to obtain a new metal alloy with ratio 17:27? (All three ratios correspond to.
17. Eight blocks Dana had the task to save the eight blocks of these rules: 1. Between two red cubes must be a different color. 2. Between two blue must be two different colors. 3. Between two green must be three different colors. 4. Between two yellow blocks must be four
18. Tachometer Tatra's tachometer shows the initial state 886123 km this morning. Tatra today travel at an average speed of 44 km/h. Determine the function that describes the Tatra's tachometer depending on the time. What is the state of tachometer after 4 hours? Two fifth-graders teams competing in math competitions - in Mathematical Olympiad and Pytagoriade. Of the 33 students competed in at least one of the contest 22 students. Students who competed only in Pytagoriade was twice more than those who just competed Two workers make 138 parts/items. The first one produces 30% more than the second. How many items will each produce?