Practice problems of the volume - page 6 of 118
Volume is the measure of the space that a body fills or occupies. The basic SI unit of volume is the cubic meter. It is the volume of a cube with an edge of one meter, i.e., 1 m x 1 m x 1 m. Significant another unit is 1 l (one liter), 1 m3 = 1000 l applies. One hectoliter (1 hl) is 100 liters.Volume is always the third power of length. Or volume = area times length. For example, the volume of the cube is a3, and the prism's volume is S*h (the area of the base times the height). The volume of rotating bodies (sphere, cone) can be derived in high school by integration. The pyramid's volume is always 1/3 of the prism's volume. We calculate the volume of the truncated bodies either with a formula or simply by subtracting the volumes of the two bodies.
Number of problems found: 2353
- Quadrilateral 83272
Calculate the surface area and volume of a regular quadrilateral pyramid whose base edge is 5 cm long and whose height is 10 cm. - Quadrilateral 83254
What is the volume of a regular quadrilateral pyramid if its base edge a = √18 cm and side edge b = 5 cm? - Calculate 83248
The cube ABCDEFGH has an edge of length 3 cm. Calculate the volume of the pyramid ABCDH. - Decimeters 83242
The axial section of the cylinder is a square with a content of 56.25 cm². Calculate its surface area and volume. Express the result in square decimeters and cubic decimeters and round to hundredths.
- Corresponding 83227
The 4m high column is a prism with a rhombus figure with an edge 80cm long and a corresponding height of 70cm. It is built of bricks. How many bricks are needed to build it if one brick has a volume of 1.4 cubic decimeters? - Dimensions 83226
Calculate the weight of an iron bar 1.2 m long, whose cross-section is a trapezoid with dimensions a=10 cm c=8 cm and the distance between the bases v=6 cm. As we know, 1 cubic meter of iron weighs 7800 kg. - Painter 83225
A painter needs to mix yellow and red paint in a ratio of 3:7. How many liters of red paint must he add to 21 liters of yellow paint? - Liters 83211
We have 160 L of water at 67°C; how many liters of cold water at 18°C are needed to cool it to 39°C? - Cylindrical 83193
How much concrete is needed to pour 8 concrete columns with a square base: a = 38 cm, the height of the columns being 6.2 m? Each column has a cylindrical cavity with a diameter of 15 cm.
- Original 83173
When drying, the modeling mass loses 36% of its original volume. If the cube's volume is 5.12 dm³ after drying, what was the original length of the edge? - Afternoon 83168
In the morning, 6 liters more water was in the green canister than in the blue one. In the afternoon, the gardener poured 1 liter of water from the green canister into the blue one. There was then twice as much water in the green canister as in the blue o - Tetrahedron 83144
A container shaped like a rotating cylinder with a base radius of 5 cm is filled with water. If a regular tetrahedron with an edge of 7 cm is immersed in it, how much will the water level in the container rise? - Dimensions 83135
The large aquarium is shaped like a cuboid and has dimensions in the ratio 5: 7: 4. The sum of the lengths of all edges is 96 dm. How many liters of water will be in the aquarium if it is filled to four-fifths? - Cylinder's 83130
Calculate the cylinder's volume if you know that the ratio of the cylinder's height to the base's radius is 3:2 and the height is 15 dm.
- Approximately 83106
The castle courtyard, with an area of 100 m², is paved with oak cubes with an edge of 8 cm. Approximately 164 bricks were used to pave m². One dm³ of oak wood weighs 0.8 kg. Calculate the weight of all the bricks used to pave the courtyard. - Distilled 83093
The 50% salt solution must be diluted with distilled water to make 20 liters of 35% solution. How many liters of original solution and how many liters of water do we need? - Calculate 83068
The internal volume of the barrel is 15 times greater than the bucket's volume. The volume of the bucket is 5 times the volume of the kettle. We took a third of the water from a barrel, leaving 60 liters in it. Calculate the volume of the kettle in liters - Completely 83045
The diesel tank has a volume of 19.6 hl. The inflow oven, which flows 17.5 l per minute, was opened for 1.5 hours. How long does the inlet pipe need to be opened for the tank to be completely filled? - Calculate 83044
The cube comprises 64 small cubes, each with an edge length of 15 mm. Calculate the wall length and body diagonals.
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