# Examples for 8th grade - page 19

1. Pizza master
Master says that he can splits pizza to 16 parts by five equals straight cuts. Is it possible?
2. Lid
What is the weight of concrete cover (lid) to round shape well with a diameter 1.8 m, if the thickness of the cover is 11 cm? 1 m3 of concrete weighs 2190 kg.
3. Elevation
What must be the elevation of an observer in order that he may be able to see an object on the earth 536 km away? Assume the earth to be a smooth sphere with radius 6378.1 km.
4. Lines
Five bus lines runs at intervals 3, 6, 9, 12, 15 minutes. In the morning, suddenly start at 4:00. After how many minutes the bus lines meet again?
5. Dices
We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
6. Fertilizer
Mr. Gherkin use for fertilization 8% solution of fertilizer. 4 liters of it still left. How much water must be added to the solution to make only 4% solution?
7. 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).
8. 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
9. 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.
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. 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?
12. 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?
13. Electronics: Resistors in parallel
From relation for calculating the resistance of parallel combination of resistors: ? Calculate the R, if R1 = 2Ω a R2 = 15Ω
14. Train from Prague
First train from Prague started at 8:00 hour at 40 kilometers per hour. Train from Ostrava started at 9:20 at 80 km per hour. In how many hours and how far from cities with trains meet if the distance of cities is 400 km.
15. Triangular prism
Calculate the surface area and volume of a triangular prism, base right triangle if a = 3 cm, b = 4 cm, c = 5 cm and height of prism h=12 cm.
16. Event probability
The probability of event P in 8 independent experiments is 0.33. What is the probability that the event P occurs in one experiment (probability is same)?
17. Two workers
The first worker completed the task by himself in 9 hours, the second in 15 hours. After two hours of joint work left first worker to a doctor and the second finished the job himself. How many hours worked second worker himself?
18. The bridge
Across the circle lakepasses through its center bridge over the lake. At three different locations on the lake shore are three fishermen A, B, C. Which of fishermen see the bridge under the largest angle?
19. Triangle KLB
It is given equilateral triangle ABC. From point L which is the midpoint of the side BC of the triangle it is drwn perpendicular to the side AB. Intersection of perpendicular and the side AB is point K. How many % of the area of the triangle ABC is area o
20. Cathethus and the inscribed circle
In a right triangle is given one cathethus long 14 cm and the radius of the inscribed circle of 5 cm. Calculate the area of this right triangle.

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