# Examples for 8th grade - page 43

1. Tank No 8 Tank is filled by one inlet valve with a flow rate of 12 liters per second in 72 minutes. How long take the tank to fill, if we open half an hour after one more inlet?
2. Shoes Peter decided to measure shoes size of his three friends. Measured accurately and wrote as follows: Venda and Jenda together 52 cm Jenda and Zdenda together 58 cm Zdenda and Venda together 54 cm a) How long measures Vendy, Jenda and Zdenda shoes together
3. Pair They have together 39 years - he has 2 times as she was when he was equal as she has today ....
4. Water reservoir The water reservoir is filled with one pump for 4 days by the second one for 9 days. Outlet can drain tank in 12 days. How long take fill the reservoir if both pumps are running and not closed outlet channel.
5. Homework Mother and Kate together weigh 24.5 kg more than the father. Father weighs 7.6 kg more than mother. Father weight 44.8 kg more than Kate. Determine weights of father mother and Kate.
6. Median In triangle ABC is given side a=10 cm and median ta= 13 cm and angle gamma 90°. Calculate length of the median tb.
7. Inscribed triangle To a circle is inscribed triangle so that the it's vertexes divide circle into 3 arcs. The length of the arcs are in the ratio 2:3:7. Determine the interior angles of a triangle.
8. Cosine The point (8, 6) is on the terminal side of angle θ. cos θ = ?
9. Three shapes 1/5 of a circle is shaded. The ratio of area if square to the sum of area of rectangle and that of the circle is 1:2. 60% of the square is shaded and 1/3 of the rectangle is shaded. What is the ratio of the area of circle to that of the rectangle?
10. Pipe How long is the pipe with an outside diameter of 1.44 m if his coloring consumed 44 kg of color. 1 kg of color coverage is 9 m2.
11. Lenka and money When Lenka bought pants from 1/3 of her savings shirt from 1/5 and 1/8 spent at the hairdresser, she is left 328 Kč. How much money was saved? How much hairdresser cost?
12. 10 pieces How to divide the circle into 10 parts (geometrically)?
13. Water level How high reaches the water in the cylindrical barell with a diameter of 12 cm if there is a liter of water? Express in cm with an accuracy of 1 decimal place.
14. Garden pool Mr. Novak fill garden pool (cylinder; diameter of 200 cm) with 31.4 hl of water. What is the depth of the pool when the water level is 10 cm below the upper edge of the pool?
15. Mine Wheel in traction tower has a diameter 5 m. How many meters will perform an elevator cabin if wheel rotates in the same direction 49 times?
16. Water pool Pool with volume 990hl completely filled, if water flows by one tap 8 hours and by second tap 6 hours. First tap give 10hl more than second per hour. How many hl flows in each of them in an hour?
17. Blackjack TU160 Bomber Tupolev TU160 started at 9:00 from the airport and flew at average speed of 1850 km/h toward the airfield B distant 3500 km. After evaluating the danger from the airport B started at 9:45 B towards A fighter MIG 29 at an average speed 2300 km/h. At
18. Triangle For how many integer values of x can 16, 15 and x be the lengths of the sides of triangle?
19. Diameter What is the inside diameter of the cylinder container and if half a liter of water reaches a height 15 cm?
20. Canister Gasoline is stored in a cuboid canister having dimensions 44.5 cm, 30 cm, 16 cm. What is the total weight of a full canister when one cubic meter of gasoline weighs 710 kg and the weight of empty canister is 1.5 kg?

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