# Volume calculator

## The volume calculator is based on several common shapes! Is this useful?

#### Volume

Volume is the most common three-dimensional solid. Volume is measured using similar-shaped natural containers, which later differs from the area, the amount of space taken up in a two-dimensional figure. The SI unit for Volume is Cubic meter m3. The Volume also refers to many things, such as:

• The degree or intensity of loudness of a sound
• The number or amount of something, which is usually a large quantity
• Formal word for a book or in a set of related books

The lists of basic shapes in Volume are listed below:

• Cone
• Cube
• Cuboid
• Cylinder
• Ellipsoid
• Sphere
• Parallelepiped
• Prism
• Pyramid
• Tetrahedron

#### Units and conversion of Volume

###### Metric volume units
• Cubic centimeters (cm3)
• Cubic meters (m3)
• Liters (l, L)
• Milliliters (ml, mL)
###### US standard, UK
• Fluid ounce (fl oz)
• Cubic inch (cu in)
• Cubic foot (cu ft)
• Cups
• Pints (pt)
• Quarts (qt)
• Gallons (gal)

#### Common Volume units

###### Unit - cubic meters - milliliters
• Milliliter - 0.000001 - 1
• Cubic inch - 0.00001639 - 16.39
• Pint - 0.000473 - 473
• Quart - 0.000946 - 946
• Liter - 0.001 - 1000
• Gallon - 0.003785 - 3785
• Cubic foot - 0.028317 - 28,317
• A cubic yard - 0.764555 - 764,555
• Cubic meter - 1 - 1,000,000
• Cubic kilometer - 1,000,000,000 - 1015

#### Volume calculator

A volume calculator calculates the Volume of common bodies based on their shapes. It is a simple tool that covers the five most popular 3D shapes. The volumes of complicated shapes can be calculated using integral calculus. An alternative method is using a volume calculator if the substance's density is known and uniform. The Volume can be calculated by using its weight. This calculator is more useful for simple shapes.

Volume calculations are useful in many sciences, construction works and planning, cargo shipping, climate control, swimming pool management, and more. All measures need to be in the same unit. Volume formulas for the most common types of geometric bodies supported by the volume calculator are described below.

#### Cube

A volume of a cube is defined as the number of cubic units by the cube completely. A cub is a 3D shape with six faces, twelve edges, and eight vertices. The Volume of a cube is the product of its length, width, and height as it is measured in cubic units. The cube is special as of shapes in geometry, including a square parallelepiped, an equilateral cuboid, and a right rhombohedron. The below equation is used to calculate the Volume of the cube:

V = a3

A - edge-length of the cube

Example:

Bob has a cubic suitcase with an edge length of 2 feet; now calculate the Volume of soil that he can carry home:

V = 23 = 8 ft3

#### Cuboid

A cuboid is a two-dimensional shape that has 4-side. The shape is formed when many congruent rectangles are placed on each other. The shape thus formed is called a cuboid. The following cuboid shows its three dimensions length, width, and height. The formula for the Volume of the cuboid is:

V = (l x b x h) cubic units

• l - length
• h - height

Example:

Find the Volume of the cuboid, which has a length of 7 inches, breadth of 5 inches, and height of 2 inches.

V = 1 x b x h = (7 x 5 x 2);

V = 70 in3

#### Cone

A cone is a three-dimensional geometric shape from a flat base to a point called the apex or vertex. The distance from the cone's vertex to the base is the height of the cone. The circular base has a measured value of radius. The length of the cone from the apex to any point on the circumference is the slant height. The cone is defined by its height, the radius of its base, and slant height.

V = 1/3 πr2h cubic units

• h - the height of the cone

Example:

Find the Volume of the cone if radius, r = 4cm, and height, h = 7cm.

V = 1/3 πr2h

V = (1/3) x (22/7) x 42 x 7

V = 117.33 Cubic Cm

#### Cylinder

The cylinder is a three-dimensional shape with a circular base. It can be seen as circular disks stacked on one another. The capacity of a cylinder box is equal to the Volume of the cylinder. The three-dimensional shape volume equals the amount of space occupied by that shape. The cylinders are connected through their centers by an axis perpendicular to the planes of their bases with a given height and radius.

V = πr2h

• h - the height of the tank

Example:

The barrels have a radius of 3 ft and height of 4 ft. Determine the Volume of sand each can hold using the Volume of cylinder formula.

V = πr2h = (22/7) x 32 x 4

V = 113.097 ft3

#### Sphere

A sphere is a three-dimensional object. The sphere is defined in the x-axis, y-axis, and z-axis. A sphere doesn't have any edges or vertices. The distance between the center and the sphere's surface are equal at any point. The distance is called the radius of the sphere. The amount of space occupied by the three-dimensional object, known as the sphere, is the Volume of the sphere.

V = 4/3 πr3 Cubic units

• r - radius of the sphere

Example:

Find the Volume of the sphere that has a diameter of 10 cm.

d = 10 cm, D = 2r units

r = d/2 = 10/2 = 5 cm

V = (4/3) x (22/7) x 53

V = 522 cubic units

#### Capsule

A capsule is a three-dimensional geometric shape comprised of a cylinder and two hemispherical ends. The Volume of the capsule can be calculated by combining the volume equations of a sphere and a right circular cylinder:

V = πr2h (4/3 r + h)

• h - the height of the cylindrical portion

Example:

A capsule with a radius of 1.5 ft and height of 3 ft determines the Volume of melted milk.

V = (22/7) x (1.5)2 x 3 [((22/7) x 1.5) + 3]

V= 35.343 ft3

#### Ellipsoid

An ellipsoid is a surface obtained from a sphere through directional scaling. It is a closed quadric surface which is a 3-D analog of an ellipse. The center of an ellipsoid is the point with three pairwise perpendicular axes of symmetry intersecting. The ellipsoid is described as tri-axial. Calculate the Volume of an ellipsoid as follows:

V = 4/3 πabc

A, b, and c - length of the axes

Example:

Xabat sandwich bun has axis lengths of 1.5 inches, 2 inches, and 5 inches. Calculate the Volume of meat he can fit in each hollowed bun as follows:

V = 4/3 x π x 1.5 x 2 x 5

V = 62.832 in3

#### Conical Frustum

The Frustum of the cone is part of the cone when it is cut by a plane into two parts. The cone's upper part remains the same, but the bottom part makes a frustum. The conical frustums in everyday life include buckets, lampshades, and drinking glasses. The formula for conical Frustum is:

V = 1/3 πh (r2 + RR + R2)

• r and R - radii of the bases
• h - the height of the Frustum

Example:

Bea is with a right conical frustum leaking ice cream. Calculate the Volume of ice cream she must quickly consume given a frustum height of 4 inches with radii of 1.5 inches and 0.2 inches.

V = 1/3 x π x 4(0.22+ 0.2 x 1.5 + 1.52)

V = 10.849 in 3

#### Prism

Prism is a three-dimensional solid object where the two ends are identical. It combines flat faces, identical bases, and equal cross-sections. The prism's bases could be triangle, square, rectangle, or n-sided polygon. The prism's Volume is defined as the product of the base area and the prism height.

V = base area x height

Example:

Find the Volume of a triangular prism when its area is 60 cm2 and height is 7 cm.

V = 60 x 7

V = 420 cm3

#### Pyramid

A pyramid is a 3D figure with a polygon base and triangular faces. The triangular sides are faces, and the point above the base is referred to as the apex. A pyramid connects each base vertex to a common apex, giving it the typical shape. The pyramid's apex is long, and its height is measured as the perpendicular distance from the plane with the base to its apex. The Volume of the pyramid is:

V = 1/3 bh

b - the area of the base

h - height

Example:

Find the Volume of the pyramid if its base area is 60 unit2 and its height is 12 units.

V = 1/3 x 60 x 12

V = 240 units3

#### Tube Pyramid

A tube is often referred to as a pipe. It is a hollow cylinder that is used to transfer fluids or gas. The tube pyramid formula involves measuring the inner and outer cylinder diameters. Calculate each of their volumes and subtract the Volume of the inner cylinder from that of the outer one. The formula for the Volume of a tube is

V = π (d12- d2 2 / 4) l

• d1 - the outer diameter
• d2< - inner diameter
• l -length of the tube

Example:

The Volume of panted low-impact concrete required building a pipe with an outer diameter of 3 feet, an inner diameter of 2.5 feet, and a length of 10 feet, and it can be calculated as

V = π (32- 2.52 / 4) x 10

V = 21.6 ft3

#### Spherical Cap

A Spherical dome is a portion of a sphere or a ball cut off by a plane. If the base area, height, and sphere radius are known, then the Volume can be found out of the particular portion. This spherical cap is also referred to as a hemisphere. The equation for calculating the Volume of a spherical cap is derived from that of a spherical segment where the radius is 0. The formula of a spherical cap is:

V = 1/3 πh2 (3R - h).

The equation converts between the height, and the radii are shown:

r and R: h = R ± √R2 - r2

r and h: R = h2 + r2/ 2h

• r - radius of the base
• R - radius of the sphere
• H - the height of the spherical cap

Example:

James's golf ball has a radius of 1.68 inches, and the height of the spherical cap that Jack cut off is 0.3 inches; the Volume can be calculated as follows:

V = 1/3 x π x 0.32 (3 x 1.68 - 0.3)

V = 0.447 in 3

#### How to use a volume calculator?

Here are steps to use the volume calculator:

• Select the type of the 3D shape - In this example, assume that you want to calculate the Volume of a cylinder.
• Choose the right section of the volume calculator - Cylinder volume.
• Type given data into proper boxes - Our cylinder has a radius of 1 ft and a height of 3 ft. You can also change the units by a click on the unit name.
• The Volume of chosen shape is displayed.

#### Measure the Volume of solids, liquids, and gases!

###### Solid

For three-dimensional objects, you can calculate the Volume by taking measurements of its dimensions and applying the appropriate volume equation. To get an exact measurement of irregular objects, follow Archimedes' footsteps as follows:

• Take a container bigger than the object you want to measure the Volume of.
• Pour water into the container.
• Put the object inside.
• The difference between the measurements is the Volume of the object.
###### Liquid

It is easy to measure the volume of liquid. The amount of liquid and degree of accuracy are the parameters to consider. The containers for baking a cake will differ from those used in chemistry. It will be different from the ones used for medical purposes.

###### Gas
• The Volume of gas is influenced by temperature and pressure. The gases expand to fill any container in which they are placed. You can also measure by using the following steps:
• Inflate a balloon with the gas you want to measure
• Check out the measures by using a device called a spirometer
• A gas syringe is used to insert or withdraw a volume of gas from a closed system.

#### Is Volume intensive or extensive?

Volume is an extensive property, the same as the amount of substance, energy, mass, or entropy. An extensive property is a measure that depends on the amount of matter. Extensive properties include a glass, a barrel, and a pool full of water with different volumes and masses. In intensive properties, containers will have the same density, refractive index, and viscosity.

#### Conclusion!

Online calculator used to calculate the Volume of geometric solids includes a capsule, cone, Frustum, cube, cylinder, hemisphere, pyramid, rectangular prism, and sphere. This volume calculator makes your calculation faster and displays the result in seconds. Make use of a volume calculator.

Determine the volume of complex shapes and common solids accurately and effortlessly with the comprehensive volume calculator provided by Allcalculator.net.

### Q: what is Volume?

Volume is a three-dimensional quantity used to measure a solid shape's capacity.

### Q. Is the Volume of a cube and a cuboid the same?

The edge length of the cube is equal to each other, whereas the cuboid is different. So a cube and a cuboid cannot have the same Volume.

### Q. Is Volume squared or cubed?

A. Volume is cubed, as it is a three-dimensional measure.

### Q. What is the difference between surface area and Volume?

A. A volume is a 3D measure, while surface area is two-dimensional.

### Q. What does volume measure?

A. Volume measures the amount of space taken up by an object in three dimensions.

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