# Grade - examples - page 10

1. Rhombus
It is given a rhombus of side length a = 29 cm. Touch points of inscribed circle divided his sides into sections a1 = 14 cm and a2 = 15 cm. Calculate the radius r of the circle and the length of the diagonals of the rhombus.
2. Present
Gift box has rectangular shape with dimensions of 8×8×3 cm. Miloslav wants to cover with square paper with sides of 18 cm. How much paper left him?
3. Mast
Mast has 17 m long shadow on a slope rising from the mast foot in the direction of the shadow angle at angle 9.3°. Determine the height of the mast, if the sun above the horizon is at angle 44°30'.
4. Sea water
Seawater contains about 4.3% salt. How many dm3 of distilled water we must pour into 5 dm3 of sea water to get water with 1.8% salt?
5. Pediatrician
Pediatrician this month of 20 working days takes 4 days holidays. What is the probability that on Monday will be at work?
Road repair took 10 days for 36 workers if they worked 9 hours a day. How many days take repair same road 37 workers if they work 8 per day?
7. Wage
Increasing the minimum wage while maintaining the other parameters of the system, unemployment will be:
8. Camp
In the camp are children. 1/2 went on a trip, 1/4 went to bathe and 38 children remained in the room. How many children are in camp?
9. Barrel of oil
Barrel of oil weighs 283 kg. When it mold 26% oil, weighed 216 kg. What is the mass of the empty barrel?
10. Rectangle
Calculate the length of the side GN and diagonal QN of rectangle QGNH when given: |HN| = 25 cm and angle ∠ QGH = 28 degrees.
11. 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
12. Cube zoom
How many percent we increase volume and surface of cube, if we magnify its edge by 38%.
13. Rectangle - sides ratio
Calculate area of rectangle whose sides are in ratio 3:13 and perimeter is 673.
14. Bricks
Brick has volume 2.2 dm3. How many bricks can drive truck with capacity 23 ton? The density of brick is 1.6 g/cm3.
15. 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.
16. 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?
17. Tare
Gross weight of shipment is 5188 kg and its tare is 5.6%. Calculate the net weight of the shipment.
18. Maximum area of rhombus
Calculate the interior angles at which equilateral rhombus has maximum area.
19. Isosceles right triangle
Calculate the area of an isosceles right triangle whose perimeter is 377 cm.
20. 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?

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