# Examples for 8th grade - page 19

1. 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?
2. 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?
3. Electronics: Resistors in parallel From relation for calculating the resistance of parallel combination of resistors: ? Calculate the R, if R1 = 2Ω a R2 = 15Ω
4. 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.
5. 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.
6. 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)?
7. 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?
8. 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?
9. 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
10. 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.
11. Box Calculate the angle between box base 9 x 14 and body diagonal length 18.
12. Do you solve this? Determine area S of rectangle and length of its sides if its perimeter is 102 cm.
13. Distance Calculate distance between two points X[18; 19] and W[20; 3].
14. Circumscribing Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
15. Workers Workers digging a jump pit in the school yard. Pit has a cuboid shape with a length 12 m, a width 20 dm and depth 36 cm. They excavate 0.4 cubic meters of soil an hour. How much time (hours and minutes) is need to the excavate this pit?
16. Balance The rod are 1.9 m long hanging weights 4 kg and 1 kg on ends. Where are centre of rod (distance from weight 4 kg) to be in balance?
17. Glass mosaic How many dm2 glass is nessesary to produc 97 slides of a regular 6-gon, whose side has length 21 cm? Assume that cutting glass waste is 10%.
18. Tank In the middle of a cylindrical tank with a bottom diameter 251 cm is standing rod which is 13 cm above the water surface. If we bank rod its end reach surface of the water just by the tank wall. How deep is the tank?
19. Inscribed rectangle The circle area is 216. Determine the area of inscribed rectangle with one side 5 long.
20. Trapezoid MO-5-Z8 ABCD is a trapezoid that lime segment CE divided into a triangle and parallelogram as shown. Point F is the midpoint of CE, DF line passes through the center of the segment BE and the area of the triangle CDE is 3 cm2. Determine the area of the trapezoid A

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