# Units - examples - page 105

1. Discount price Coat cost 150 euros after sales discount. What is the original price when the discount is 25% of the original price?
2. Barrel with water The water barrel has a weight of 52 kg. When we pour a quarter of the water, the weight of the barrel is reduced to 40 kg. Determine the weight of the empty barrel. The railroad runs parallel to the railway. The train travels at 36 km/h on track. In the opposite direction, the motorcycle rides at 90 km/h. The train passes in 3 seconds. How long is a train?
4. Square Calculate the area of the square shape of the isosceles triangle with the arms 50m and the base 60m. How many tiles are used to pave the square if the area of one tile is 25 dm2?
5. Mushrooms Mushrooms lose 90% by weight drying. How many fresh mushrooms are needed for 5 kg of dried mushrooms?
6. Axial cut of a rectangle Calculate the volume and surface of the cylinder whose axial cut is a rectangle 15 cm wide with a diagonal of 25 cm long.
7. Soup from canteen For how many people is 90 liters of soup enough if we assume 3/8 liter of soup per person in the canteen?
8. Summer tires Three tire servants have to change the summer tires on 6 cars in 2 hours. Mark's replacement would take 4.5 hours, Jirka would do it in 3 hours and 10 minutes, and Honza in 4 hours. Will they be able to replace all tires at the desired time?
9. Rectangles How many different rectangles with sides integers (in mm) have a circumference exactly 1000 cm?
10. Cube into cylinder If we dip a wooden cube into a barrel with a 40cm radius, the water will rise 10 cm. What is the size of the cube edge?
11. The cube The cube has an edge of 25 cm. We cut it into small cubes of 5 cm long side. How many of these little ones left when we build a new cube of 20 cm in length?
12. Bottle A company wants to produce a bottle whose capacity is 1.25 liters. Find the dimensions of a cylinder that will be required to produce this 1.25litres if the hight of the cylinder must be 5 times the radius.
13. Pool tiles The pool is 25m long, 10m wide and 160cm deep. How many m2 of tiles will be needed on the walls and the pool? How many pieces of tile are needed when 1 tile has a square shape with a 20cm side? How much does it cost when 1m2 of tiles costs 258 Kc?
14. Three segments The circle is divided into 3 segments. Segment A occupies 1/4 of the area, segment B occupies 1/3 of the area. What part is occupied by section C? In what proportion are areas A: B: C?
15. Hectares The tractor plows the first day of 4.5ha, the second day 6.3ha and the third day 5.4ha. It worked whole hours a day, and its hourly performance did not change and was the highest of the possible. How many hectares did it plow in one hour (what is it perfor
16. Right triangle Ladder 16 feet reaches up 14 feet on a house wall. The 90-degree angle at the base of the house and wall. What are the other two angles or the length of the leg of the yard?
17. Depth angle From a cliff of 150 meters high, we can see the ship at a depth angle of 9° at sea. How far is the ship from the cliff?
18. Resistance A resistor having an electrical resistance of 1.5 k ohms passes an electrical current of 0.1 A. Calculate what voltage is between the terminals of the resistor.
19. A residential A residential colony has a population of 5400 and 60 litres of water is required per person per day. For the effective utilization of rain water, they constructed a water reservoir measuring 48m × 27m × 25m to collect the rain water. For how many days, the
20. Circle simple Circumference of a circle is 6.28. What is the area of the circle?

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