# Volume - 7th grade (12y) - examples

1. 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?
2. Prism 4 sides
Find the surface area and volume four-sided prism high 10cm if its base is a rectangle measuring 8 cm and 1.2dm
3. Rectangular cuboid
The rectangular cuboid has a surface area 5334 cm2, its dimensions are in the ratio 2:4:5. Find the volume of this rectangular cuboid.
4. Pool
The swimming pool is 10 m wide and 8 m long and 153 cm deep. How many hectoliters of water is in it, if the water is 30 cm below its upper edge?
5. Cylinders
Area of the side of two cylinders is same rectangle of 50 cm × 11 cm. Which cylinder has a larger volume and by how much?
6. Tanks
Fire tank has cuboid shape with a rectangular floor measuring 13.7 m × 9.8 m. Water depth is 2.4 m. Water was pumped from the tank into barrels with a capacity of 2.7 hl. How many barrels were used, if the water level in the tank fallen 5 cm? Wr
7. Alcohol
How many 55% alcohol we need to pour into 14 liters 75% alcohol to get p3% of the alcohol? How many 65% alcohol we get?
8. Density - simple example
Material of density of 532 kg/m3 occupies a container volume of 79 cm3. What is its mass?
9. Water
Mix 21 l of water with temperature of 38 °C, 67 l warm of 34 °C and 14 l water of 32 °C. What is the temperature of the mixed water immediately after mixing?
10. 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?
11. 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?
12. 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.
13. Sea water
Mixing 34 kg of sea water with 34 kg rainwater is created water containing 3.4% salt. How many percent sea water contains salt?
14. 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.
15. 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.
16. Car range
Calculate the maximum range of car, if you can spend 10 euros, price of diesel is 1.55 Eur/l and car consumption is 3 l/100 km.
17. The pot
The pot is in 1/3 filled with water. Bottom of the pot has an area of ​​329 cm2. How many centimeters rises water level in the pot after add 1.2 liters of water?
18. Cube
The cube weighs 11 kg. How weight is cube of the same material, if its dimensions are 3-times smaller?
19. Air
Room is 40.1 m long, 25.2 dm wide and 369 cm high. How many people can simultaneously be in this room if for hygiene reasons is calculated 5100 dm3 of air per person?
20. Pool
Mr. Peter build a pool shape of a four-sided prism with rhombus base in the garden. Base edge length is 8 m, distance of the opposite walls of the pool is 7 m. Estimated depth is 144 cm. How many hectoliters of water consume Mr. Peter to fill the pool?

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