# Grade - examples - page 34

1. Circular sector I have a circular sector with a length 15 cm with an unknown central angle. It is inscribed by a circle with radius 5 cm. What is the central angle alpha in the circular sector?
2. Sea How far can you see from the ship's mast, whose peak is at 14 meters above sea level? (Earth's radius is 6370 km).
3. Denominator Calculate the missing denominator x: ?
4. Glass of juice Glass of juice shaped cylinder 16 cm height and base diameter of 7 cm is filled with juice so that the level is 4 cm below the rim of the glass. Determine the maximum angle of the cup can be tilted and juice don't overflow.
5. Cinema Cinema auditorium is built for 3300 people. The first row is planned for 36 seats and each next gradually 4 more. How many rows of seats will have auditorium?
6. Pedestrian and cyclist Pedestrian out with a speed of 4 km/hour from city center and after 1hour and 10 minutes came after him cyclist at speed of 18 km/h. At how many minutes he catches up with pedestrian?
7. Purchase Mother bought 5 boxes of milk and 7 kg of potatoes and paid a total CZK 147. Aunt bought 7 boxes of milk and 3 kg of potatoes and paid 131 CZK. What is the price of one carton of milk and 1 kg of potatoes? How CZK together would have saved if bought at the
8. Dices We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
9. Euclid2 In right triangle ABC with right angle at C is given side a=27 and height v=12. Calculate the perimeter of the triangle.
10. Cyclist A cyclist is moving at 35 km/h and follow pedestrian who is walking at speed 4 km/h. Walker has an advantage 19 km. How long take cyclist to catch up with him?
11. N-gon How many diagonals has convex 11-gon?
12. Carpenter You want to cut long board into smaller pieces. Carpenter said that one cut of the board into two pieces will cost you 100 cents. But you need to cut the board into 9 parts. How much you pay?
13. Circle in rhombus In the rhombus is inscribed circle. Contact points of touch divide the sides to parts of length 19 cm and 6 cm. Calculate the circle area.
14. School 27 students of 6.D class is going to a trip. They pay 9 € each. The teacher got 153 €. How many children have not paid?
15. Tiles Hall has dimensions 325 &time; 170 dm. What is the largest size of square tiles that can be entire hall tiled and how many we need them?
16. Electronics: Resistors in parallel From relation for calculating the resistance of parallel combination of resistors: ? Calculate the R, if R1 = 2Ω a R2 = 15Ω
17. Hiker Hiker went half of trip the first day, the third of trip the second day and remaines 15 km. How long trip he planned?
18. Plasticine ball Plasticine balls have radius r1=85 cm, r2=60 mm, r3=59 cm, r4=86 cm, r5=20 cm, r6=76 mm, r7=81 mm, r8=25 mm, r9=19 mm, r10=14 cm. For these balls.
19. Water tank Water tank shape cuboid has a width of 3.1 m and length twice larger. How high will reach water if water flow into 13 liters of water per second during 16 minutes?
20. Exhibition The teacher paid for 280 Kč for 4.A students for admission to the exhibition. How many students were on the exhibition?

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.