# Examples for 9th grade - page 5

1. Diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
2. Pipes Water pipe has a cross-section 1087 cm2. An hour has passed 960 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 9 hours if water flow same speed?
3. Area of RT Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5.
4. Eiffel Tower Eiffel Tower in Paris is 300 meters high, is made of steel. Its weight is 8000 tons. How tall is the tower model made ​​of the same material, if it weigh is 2.4 kg?
5. Ace From complete sets of playing cards (32 cards), we pulled out one card. What is the probability of pulling the ace?
6. Flags How many different flags can be made from colors white, red, green, purple, orange, yellow, blue so that each flag consisted of three different colors?
7. Two cars Two cars started against each other at the same time to journey long 293 km. First car went 41 km/h and second 41 km/h. What distance will be between this cars 20 minutes before meet?
8. Forces In point O acts three orthogonal forces: F1 = 20 N, F2 = 7 N and F3 = 19 N. Determine the resultant of F and the angles between F and forces F1, F2 and F3.
9. Circles The areas of the two circles are in the ratio 2:20. The larger circle has diameter 20. Calculate the radius of the smaller circle.
10. Cylinders Area of the side of two cylinders is same rectangle of 33 mm × 18 mm. Which cylinder has a larger volume and by how much?
11. MO SK/CZ Z9–I–3 John had the ball that rolled into the pool and it swam in the water. Its highest point was 2 cm above the surface. Diameter of circle that marked the water level on the surface of the ball was 8 cm. Determine the diameter of John ball.
12. Widescreen monitor Computer business hit by a wave of widescreen monitors and televisions. Calculate the area of ​​the LCD monitor with a diagonal size 20 inches at ratio 4:3 and then 16:9 aspect ratio. Is buying widescreen monitors with same diagonal more advantageous tha
13. Tanks Fire tank has cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wr
14. Vans In how many ways can 9 shuttle vans line up at the airport?
15. Circle arc Circle segment has a circumference of 135.26 dm and 2096.58 dm2 area. Calculate the radius of the circle and size of central angle.
16. Square diagonal Calculate length of the square diagonal if the perimeter is 476 cm.
17. Numbers Determine the number of all positive integers less than 4183444 if each is divisible by 29, 7, 17. What is its sum?
18. Right Determine angles of the right triangle with the hypotenuse c and legs a, b, if: ?
19. Seating How many ways can 5 people sit on 4 numbered chairs (e. G. , seat reservation on the train)?
20. Tractors Fields go plow two tractors with various performance. The first tractor plow whole field in 11 hours, the second tractor plow whole field 19 hours longer. How long take plow whole field with two tractors?

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