# Grade - examples - page 13

1. 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.
2. Earth parallel
Earth's radius is 6370 km long. Calculate the length parallel of latitude 50°.
3. Floor
The floor area of ​​the room is 31 m2 and has a width of 4.3 m. How many centimeters of circumference measured floor on the map at the scale 1:75?
4. Arc
Circle arc corresponding to angle is 32° is 28 dm long. What is the length of the entire circle?
5. Guests
How many ways can 5 guests sit down on 6 seats standing in a row?
6. Circular pool
The base of pool is circle with a radius r = 10 m excluding circular segment that determines chord length 10 meters. Pool depth is h = 2m. How many hectoliters of water can fit into the pool?
7. 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.
8. Laws
From which law follows directly the validity of Pythagoras' theorem in the right triangle? ?
9. 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?
10. Similarity
Are two right triangles similar to each other if the first one has a acute angle 70° and second one has acute angle 20°?
11. 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?
12. Milimeters
How many millimeters is 1/4 meters?
13. Diagonal
Determine the dimensions of the cuboid, if diagonal long 53 dm has angle with one edge 42° and with other edge 64°.
14. Rotation
Right triangle with legs 14 cm and 20 cm rotate around longer leg. Calculate the volume and surface area of the formed cone.
15. Described
Calculate perimeter of the circle described by a triangle with sides 478, 255, 352.
16. 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.
17. 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°?
18. Reciprocal
For given real numbers, calculate reciprocal number.
19. Balls
I have 19 balls and my friend has 27. About how many has my friend more balls?
20. Trapezoid
Calculate area of trapezoid ABCD with sides |AD|= 57 cm, |DC|=30 cm, |CB|=7 cm, |AB|=40 cm..

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