# Examples for 8th grade - page 7

1. Engineer Kažimír The difference between politicians-demagogues and reasonable person with at least primary education beautifully illustrated by the TV show example. "Engineer" Kažimír says that during their tenure there was a large decline in the price of natural gas, pri
2. Cube zoom How many percents do we increase the volume and surface of the cube if we magnify its edge by 38 %?
3. Rectangle - sides ratio Calculate area of rectangle whose sides are in ratio 3:13 and perimeter is 673.
4. Rhombus and inscribed circle It is given a rhombus with side a = 6 cm and the radius of the inscribed circle r = 2 cm. Calculate the length of its two diagonals.
5. Car Car goes from point A to point B at speed 86 km/h and back 53 km/h. If they goes there and back at speed 67 km/h trip would take 10 minutes shorter. What is distance between points A and B?
6. Tare Gross weight of shipment is 5188 kg and its tare is 5.6%. Calculate the net weight of the shipment.
7. Maximum area of rhombus Calculate the interior angles at which equilateral rhombus has a maximum area.
8. Isosceles right triangle Calculate the area of an isosceles right triangle whose perimeter is 377 cm.
9. Gear Two gears, fit into each other, has transfer 2:3. Centres of gears are spaced 82 cm. What are the radii of the gears?
10. Rectangle In rectangle ABCD with sides |AB|=19, |AD|=16 is from point A guided perpendicular to the diagonal BD, which intersects at point P. Determine the ratio ?.
11. Cone Circular cone of height 15 cm and volume 5699 cm3 is at one-third of the height (measured from the bottom) cut by a plane parallel to the base. Calculate the radius and circumference of the circular cut.
12. Motion Cyclist started at 9:00 from point S to point T. After 10 minutes, followed him at the same speed the second cyclist. Walker, which went from T to S, started at 9:35. After 71 minutes he met the first cyclist and after next 8 minutes the second cyclist. Di
13. Daily average Calculate the average temperature during the day, when 15 hours was 20 °C and 9 hours was 13 °C.
14. Expansion If one side of the rectangle is larger 4-times and second 2-times, what percentage increases the area of rectangle?
15. Tangents To circle with a radius of 41 cm from the point R guided two tangents. The distance of both points of contact is 16 cm. Calculate the distance from point R and circle centre. Convert 270° to radians. Write result as multiple of number π.
17. Sea water Mixing 62 kg of sea water with 84 kg rainwater is created water containing 3.1% salt. How many percent sea water contains salt?
18. Lathe From the cube of edge 37 cm was lathed maximum cylinder. What percentage of the cube is left as waste after lathed?
19. Cu thief The thief stole 122 meters copper wire with cross-section area of 95 mm2. Calculate how much money gets in the scrap redemption, if redeemed copper for 5.5 eur/kg? The density of copper is 8.96 t/m3.
20. Guests How many ways can 9 guests sit down on 11 seats standing in a row?

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