# Volume - problems

1. Prism 4 sides
The prism has a square base with a side length of 3 cm. The diagonal of the sidewall of the prism/BG/is 5 cm. Calculate the surface of this prism in cm square and the volume in liters
2. 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?
3. The diagram 2
The diagram shows a cone with slant height 10.5cm. If the curved surface area of the cone is 115.5 cm2. Calculate correct to 3 significant figures: *Base Radius *Height *Volume of the cone
4. 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
5. Pile of sand
A large pile of sand has been dumped into a conical pile in a warehouse. The slant height of the pile is 20 feet. The diameter of the base of the sand pile is 31 feet. Find the volume of the pile of sand.
6. Pool
If water flows into the pool by two inlets, fill the whole for 18 hours. First inlet filled pool 6 hour longer than second. How long pool is filled with two inlets separately?
7. TV transmitter
The volume of water in the rectangular swimming pool is 6998.4 hectoliters. The promotional leaflet states that if we wanted all the pool water to flow into a regular quadrangle with a base edge equal to the average depth of the pool, the prism would have.
8. Cube in a sphere
The cube is inscribed in a sphere with volume 6116 cm3. Determine the length of the edges of a cube.
9. Axial section
Axial section of the cone is equilateral triangle with area 208 dm2. Calculate volume of the cone.
10. 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.
11. Cuboid
Cuboid with edge a=16 cm and body diagonal u=45 cm has volume V=11840 cm3. Calculate the length of the other edges.
12. 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?
13. Cubes
One cube is inscribed sphere and the other one described. Calculate difference of volumes of cubes, if the difference of surfaces in 257 mm2.
14. Transforming cuboid
Cuboid with dimensions 8 cm, 13 and 16 cm is converted into a cube with the same volume. What is its edge length?
15. Sphere
Surface of the sphere is 2820 cm2, weight is 71 kg. What is its density?
16. Pipes
Water pipe has a cross-section 1087 cm2. An hour has passed 960 m3 of water. How much water flows through the pipe with cross-section 300 cm2 per 9 hours if water flow same speed?
17. 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?
18. 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
19. 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?
20. Density - simple example
Material of density of 532 kg/m3 occupies a container volume of 79 cm3. What is its mass?

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