# Examples for 9th 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. Triangular prism The base perpendicular triangular prism is a right triangle whose hypotenuse measures 5 cm and one cathetus 2 cm. Height of the prism is equal to 7/9 of the perimeter of the base. Calculate the surface area of prism.
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. 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.
5. 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.
6. Car factory Carmaker now produce 2 cars a day more than last year, so the production of 70312 cars will save just one full working day. How many working days needed to manufacture 70312 cars last year?
7. 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.
8. 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)?
9. Lord Ram When lord Ram founded the breed white sheep was 8 more than black. Currently white sheep are four times higher than at the beginning and black three times more than at the beginning. White sheep is now 42 more than the black. How many white and black sh
10. 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?
11. MO circles Juro built the ABCD square with a 12 cm side. In this square, he scattered a quarter circle that had a center at point B passing through point A and a semicircle l that had a center at the center of the BC side and passed point B. He would still build a ci
12. 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
13. 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.
14. Subsets How many are all subsets of set ??
15. Machine Price of the new machine is € 62000. Every year is depreciated 15% of residual value. What will be the value of the machine after 3 years?
16. Distance Calculate distance between two points X[18; 19] and W[20; 3].
17. Circumscribing Determine the radius of the circumscribed circle to the right triangle with legs 9 cm and 6 cm.
18. 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?
19. 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?
20. 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%.

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