# Examples for 8th grade - page 8

1. Guests How many ways can 9 guests sit down on 11 seats standing in a row?
2. Arc Circle arc corresponding to angle is 32° is 28 dm long. What is the length of the entire circle?
3. Circular pool The base of the pool is a circle with a radius r = 10 m, excluding a circular segment that determines the chord length 10 meters. The pool depth is h = 2m. How many hectoliters of water can fit into the pool?
4. Floating barrel Barrel (cylinder shape) floats on water, top of barrel is 8 dm above water and the width of surfaced barrel part is 23 dm. Barrel length is 24 dm. Calculate the volume of the barrel.
5. Birthdate Jane on birthday brought 30 lollipops and 24 chewing gum for their friends. How many friends has, if everyone receives the same number of lollipops and chewing gums? How much chewing gum and lollipops got any friend?
6. Pedestrian up-down hill Pedestrian goes for a walk first at plane at 4 km/h, then uphill 3 km/h. Then it is in the middle of the route, turns back and goes downhill at speed 6 km/h. Total walk was 6 hours. How many kilometers went pedestrian?
7. Rotation The right triangle with legs 14 cm and 20 cm rotate around the longer leg. Calculate the volume and surface area of the formed cone.
8. Described Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
9. Medians Calculate the sides of a right triangle if the length of the medians to the legs are ta = 21 cm and tb=12 cm.
10. Kites Boys run kite on a cable of 68 meters long. What is the kite altitude, if the angle from the horizontal plane is 72°?
11. Trapezoid Calculate area of trapezoid ABCD with sides |AD|= 68 cm, |DC|=35 cm, |CB|=12 cm, |AB|=35 cm.. Ladder 8 m long is leaning against the wall. Its foot is 1 m away from the wall. In which height ladder touches the wall?
13. VAT John paid 100 Euros in store for purchase. Calculate value added tax (VAT), which paid in purchase, if the VAT rate is 20%.
14. One half One half of ? is: ?
15. R Trapezium Rectangular trapezium has bases 12 and 5 and area 84 cm2. What is its perimeter?
16. Air mass What is the weight of the air in a classroom with dimensions 10 m × 10 m × 2.7 m ? The air density is 1.293 kg/m3.
17. The cyclist The cyclist went from village to town. First half of journey went at 20 km/h. The second half of the journey, which mostly fell, went at 39 km/h. All journey took 88 minutes. Calculate the distance from the village to the town.
18. Gear wheels Two gear wheels, which fit together have the number of teeth z1=58 and z2=149. Calculate the speed of the first wheel, if the second wheel rotates 1232 revolutions per minute.
19. Arc and segment Calculate the length of circular arc l, area of the circular arc S1 and area of circular segment S2. Radius of the circle is 33 and corresponding angle is ?.
20. Triangle Can be rectangular triangle equilateral?

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