# Examples for 9th grade - page 18

1. Mystery of stereometrie Two regular tetrahedrons have surfaces 88 cm2 and 198 cm2. In what ratio is their volumes? Write as a fraction and as a decimal rounded to 4 decimal places.
2. Pumps Pump that draws water at velocity 3.5 liters per second water from a construction trench take 35 minutes. a) Find out how many minutes the water would run out of the trench pump that draws 7.4 liters of water per second. b) What is the pumping velocity wo
3. Lock Combination lock will open when the right choice of 5 numbers (from 1 to 12 inclusive) is selected. A. How many different lock combinations are possible? B. Is he combination lock named appropriately?
4. Compass What angle are between directions WSW (WestSouthWest) and SSE (SouthSouthEast) on the compass?
5. 3y inflation Price of the roll rise in the first year by 9%, the second year fell by 5% and in the third year increased by 3%. Calculate the average annual increase in price of the roll.
6. Pit Pit has shape of a truncated pyramid with rectangular bases and is 0.8 m deep. The length and width of the pit is the top 3 × 1.5 m bottom 1 m × 0.5 m. To paint one square meter of pit we use 0.6 l of green colour. How many liters of paint is needed when w
7. Cuboid Find the cuboid that has the same surface area as the volume.
8. Height difference What height difference overcome if we pass road 1 km long with a pitch21 per mille?
9. AVG of INT What is the average of the integers from 9 throuht 52 inclusive?
10. Black building Keith built building with a rectangular shape 6.5 m × 3.9 m. Calculate how much percent exceeded the limit 25 m2 for small building. Building not built in accordance with the law is called "black building". Calculate the angle that the walls were clenchin Average climb of the road is given by ratio 1:15. By what angle road average climb?
12. 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.
13. 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.
14. Dices We will throw two dice. What is the probability that the ratio between numbers on first and second dice will be 1:2?
15. Triangle and its heights Calculate the length of the sides of the triangle ABC, if va=5 cm, vb=7 cm and side b is 5 cm shorter than side a.
16. 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?
17. 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?
18. 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.
19. 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).
20. 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

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