# Examples for 9th grade - page 66

1. Right triangle eq2 Hypotenuse of a right triangle is 9 cm longer than one leg and 8 cm longer than the second leg. Determine the circumference and area of a triangle.
2. The factory The factory ordered 500 hexagonal steel bars of square section with 25 mm side. How many cars with a load capacity of 3 tonnes will be needed for bars move if the steel density is 7,850 kg.m-3?
3. Sweets We want to prepare 5 kg of sweets for 150 CZK. We will mix cheaper candy: 1 kg for 120 CZK and more expensive candy: 1 kg per 240 CZK. How much of this two types of candy is necessary to prepare this mixture?
4. Rectangle - sides 4 Perimeter of the rectangle is 72 cm. Calculate the length of the sides that are in the ratio 3:5.
5. Unknown number 10 Number first increased by 30%, then by 1/5. What percentage we've increased the original number?
6. Pet store In a pet store, they are selling out the fish from one aquarium. Ondra wanted half of all fish, but they don't wish cut by hal fany fish he got one more than demanded. Matthew wished the remaining half of the fish, but as Andrew got half the fish more th
7. Steamer At 6 hours 40 minutes steamer sailed from the port at speed 12 km/h. At exactly 10 hours started sail motorboat at speed 42 km/h. When motorboat will catch steamer?
8. Rotary bodies The rotating cone and the rotary cylinder have the same volume 180 cm3 and the same height v = 15 cm. Which of these two bodies has a larger surface area?
9. Hydrochloric acid Determine the concentration of which must have a solution of hydrochloric acid that mixing 10 l of the solution with 8 liters of 26% solution to get the solution with a concentration of 50%?
10. Three ints The sum of three consecutive integers is 2016. What numbers are they?
11. Skiing meeting On the skiing meeting came four friends from 4 world directions and led the next interview. Charles: "I did not come from the north or from the south." Mojmir "But I came from the south." Joseph: "I came from the north." Zdeno: "I come from the south." W
12. Circular lawn Around a circular lawn area is 2 m wide sidewalk. The outer edge of the sidewalk is curb whose width is 2 m. Curbstone and the inner side of the sidewalk together form a concentric circles. Calculate the area of the circular lawn and the result round to 1
13. Prism - eq triangle Calculate the volume and surface of the prism with the base of an equilateral triangle with side a = 4cm and the body height is 6cm.
14. Eight palm There grows 8 palms by the sea. At the first sitting one parrot, on second two, on third sits four parrots on each other twice the previous parrots sitting on a previous palm. How many parrots sitting on eighth palm?
15. Octahedron All walls of regular octahedron are identical equilateral triangles. ABCDEF octahedron edges have a length d = 6 cm. Calculate the surface area and volume of this octahedron.
16. Roof tiles The roof has a trapezoidal shape with bases of 15 m and 10 m, height of roof is 4 meters. How many tiles will need if on 1 m2 should be used 8 tiles?
17. Forces Determine the resultant of two perpendicular forces F1 = 560 N and second force of 25% smaller.
18. Seamstress 2 Seamstress bought two kinds of textile in whole meters. One at 50 SKK and the second 70 SKK per meter. How many meter bought from this two textiles when paid totally 1540 SKK?
19. Umbrella Can umbrella 75 cm long fit into a box of fruit? The box has dimensions of 390 mm and 510 mm.
20. PIN - codes How many five-digit PIN - code can we create using the even numbers?

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