Body volume - 7th grade (12y) - examples

1. Sphere VS Find the surface and volume of a sphere that has a radius of 2 dm.
2. Metal tube Calculate the metal tube mass 8dm long with the outer radius 5cm and the inner radius 4.5cm and 1cm3 of this metal is 9.5g.
3. Winch The steel rope has a diameter of 6mm and a length of 20m. We are winding on drum width 60mm, starting diameter 50mm. What is the final diameter after winding?
4. Iceberg What is the surface area of 50 cm iceberg (in the shape of a cuboid) that can carry a man with luggage with a total weight of 120 kg?
5. Triangular prism Calculate a triangular prism if it has a rectangular triangle base with a = 4cm and hypotenuse c = 50mm and height of the prism is 0.12 dm.
6. 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?
7. 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.
8. 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?
9. Tereza The cube has area of base 256 mm2. Calculate the edge length, volume and area of its surface.
10. 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?
11. 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
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. 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.
14. 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?
15. Cube The cube weighs 11 kg. How weight is cube of the same material, if its dimensions are 3-times smaller?
16. 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?
17. 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?
18. Cu wire Copper wire has a length l = 980 m and diameter d = 8 mm. Calculate the weight if density of copper is ρ = 8500 kg/m3. Result round to one decimal place.
19. Cubes Cube, which consists of 27 small cubes with edge 4 dm has volume:
20. Cylinder Calculate the dimensions of rotating cylindrical container with volume 2 l, if height of container is equal to the diameter of the base.

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