# Examples for 8th grade - page 41

1. 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.
2. 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?
3. Daughters
The man conducting the census asks a woman to age of three daughters. Woman says when multiply the age getnumber 72; if their ages add up, get a number of our house, as you see. The man says: That is not enough to calculate their ages. She says: my oldes
4. 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.
5. Equator
Suppose that tourist went on foot over the Globe equator. How many meters more track made ​​his hat on his head as the shoes on your feet? The radius of the earth is 6378 km and height of the tourist is 1.7 m.
6. Acute angles
Sizes of acute angles in the right-angled triangle are in the ratio 1: 3. What is size of the larger of them?
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. For thinkings
The glass cube dive into the aquarium, which has a length of 25 cm, width 20 cm and height of 30 cm. Aquarium water rises by 2 cm. a) What is the volume of a cube? b) How many centimeters measure its edge?
10. Square Number
If to a square of integer number add 31, we get the square of next integer number. What is the original number?
11. Arc
What area of a circle occupied the flowers planted in the arc of a circle with radius 4 m with central angle 45°?
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. Barrel with liquid
Barrel with grain weight 297 kg. When it shed 48% of grain, ha weight 174 kg. What is the weight of empty barrel?
17. 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
18. Floating floor
In the new building is considered a floating floor worker in each room. 30 minutes lay 9 m2 of the floor. How long 3 workers laid the floor in 4 rooms with a total area of 90 m2?
19. 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.
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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