# Examples for 8th grade - page 4

1. Cube diagonal Determine the length of the cube diagonal with edge 75 mm.
2. Regular 5-gon Calculate area of the regular pentagon with side 7 cm.
3. Tereza The cube has area of base 256 mm2. Calculate the edge length, volume and area of its surface.
4. Logs Trunk diameter is 52 cm. Is it possible to inscribe a square prism with side 36 cm?
5. Sphere The surface of the sphere is 12100 cm2, and weight is 136 kg. What is its density?
6. Right triangle Alef The obvod of a right triangle is 84 cm, the hypotenuse is 37 cm long. Determine the lengths of the legs.
7. Rectangle In rectangle with sides, 6 and 3 mark the diagonal. What is the probability that a randomly selected point within the rectangle is closer to the diagonal than to any side of the rectangle?
8. No. of divisors How many different divisors have number ??
9. Square and circles Square with sides 83 cm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
10. Motion2 Cyclist started out of town at 19 km/h. After 0.7 hours car started behind him in the same direction and caught up with him for 23 minutes. How fast and how long went car from the city to caught cyclist?
11. Proof PT Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
12. ŽSR Calculate fixed annual personnel costs of operating monorail line 118 km long if every 5 km is station, which serve three people - one dispatcher and two switchman in 4-shift operation. Consider the average salary of the employee 885 €.
13. Vinegar 2 How many percentage of getvinegar solution, if we mix to 3.5 liters of 5.8% and 5 liters of 7.6% vinegar?
14. Rhombus ABCD Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
15. Diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
16. Area of RT Calculate the area of a right triangle that hypotenuse has length 14, and one hypotenuse segment has length 5.
17. 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?
18. Ace From complete sets of playing cards (32 cards), we pulled out one card. What is the probability of pulling the ace?
19. 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?
20. 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?

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