# Examples for 9th grade - page 39

1. Two boxes-cubes Two boxes cube with edges a=38 cm and b = 81 cm is to be replaced by one cube-shaped box (same overall volume). How long will be its edge?
2. Sphere vs cube How many % of the surface of a sphere of radius 12 cm is the surface of a cube inscribed in this sphere?
3. Concentric circles In the circle with diameter 19 cm is constructed chord 9 cm long. Calculate the radius of a concentric circle that touches this chord.
4. Motion 2 At 10 o'clock started from place A car speed at 90 km/h. 20 minutes after started from the place B at speed 60 km/h another car. Distance places A and B is 120 kilometers. What time and where they meet?
5. Nuts, girl and boys Milena collected fallen nuts and called a bunch of boys let them share. She took a condition: the first boy takes one nut and tenth of the rest, the second takes 2 nuts and tenth new rest, the third takes 3 nuts and tenth new rest and so on. Thus managed.
6. 3d vector component The vector u = (3.9, u3) and the length of the vector u is 12. What is is u3?
7. Freight and passenger car The truck starts at 8 pm at 30 km/h. Passenger car starts at 8 pm at 40 km/h. Passenger arrives in the destination city 1 hour and 45 min earlier. What is the distance between the city of departure and destination city?
8. Digging companies Company A would dig a pit for 12 days, company B for 15 days, company C for 20 days and the company D for 24 days. Work began together companies C and D, but after three days joined them other two companies. How long took to dig a pit?
9. Square Number If to a square of integer number add 31, we get the square of next integer number. What is the original number?
10. Arc What area of a circle occupied the flowers planted in the arc of a circle with radius 4 m with central angle 45°?
11. Golden ratio Divide line of length 14 cm into two sections that the ratio of shorter to greater is same as ratio of greater section to whole length of the line.
12. Round table Round table with diameter d = 105 cm is coated by square tablecloth with a side length 121 cm. About how many cm is higher center of tablecloth than its cornes?
13. Mr Novak Mr Novak earns an average 1249 euros. When increasing the salary they gave him a choice: ? What is better choice for Mr Novak?
14. Nuts How many we must have at least nuts if we can equally divide it to 10 children, 11 children or 19 children and any nut left?
15. Ski lessons On the ski course leaves 80 pupils. They live in triple and quadruple rooms. Count if rooms is the 23. How many are triple and quadruple rooms?
16. Cups We have three cups. In the cups we had fluid and boredom we started to shed. 1 We shed one-third of the fluid from the second glass into the first and third. 2 Then we shed one quarter cup of liquid from the first to the second and to the third. 3 Then
17. Circle tangent It is given to a circle with the center S and radius 3.5 cm. Distance from the center to line p is 6 cm. Construct a circle tangent n which is perpendicular to the line p.
18. Tetrahedral prism The height of a regular tetrahedral prism is three times greater than the length of the base edge. Calculate the length of the base edge, if you know that the prism volume is 2187 cm3.
19. Three-digit How many three-digit natural numbers is greater than 321 if no digit in number repeated?
20. Inflow - outflow The tank will fill by inflow for 143 minutes and empties by outflow for 150 minutes. How long take to fill tank if it is also opened the inflow and outflow?

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