# Examples for 8th grade - page 5

1. Sphere Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
2. Rectangle In rectangle with sides 10 and 8 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?
3. No. of divisors How many different divisors has number ??
4. Square and circles Square with sides 61 mm is circumscribed and inscribed with circles. Determine the radiuses of both circles.
5. 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?
6. Proof PT Can you easy prove Pythagoras theorem using Euclidean theorems? If so, do it.
7. 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 €.
8. Rhombus ABCD Rhombus ABCD, |AC| = 90 cm, |BD| = 49 cm. Calculate the perimeter of the rhombus ABCD.
9. Vinegar 2 How many percentage of getvinegar solution, if we mix to 2 liters of 5.9% and 2 liters of 3.5% vinegar?
10. Diagonal Calculate the length of the diagonal of the rectangle ABCD with sides a = 8 cm, b = 7 cm.
11. 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?
12. Area of RT Calculate the area of a right triangle which hypotenuse has length 10 and one hypotenuse segment has lenght 5.
13. Ace From complete sets of playing cards (32 cards) we pulled out one card. What is the probability of pulling the ace?
14. 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?
15. 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.
16. 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.
17. Cylinders Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
18. 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?
19. Reverse Pythagorean theorem Given are lengths of the sides of the triangles. Decide which one is rectangular: Δ ABC: 77 dm, 85 dm, 36 dm ? Δ DEF: 55 dm, 82 dm, 61 dm ? Δ GHI: 24 mm, 25 mm, 7 mm ? Δ JKL: 32 dm, 51 dm, 82 dm ? Δ MNO: 51 dm, 45 dm, 24 dm ?
20. 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

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