## What is Volume?

Volume marked *V*; size defines the number of units of space covered by a body. The unit of volume is the cubic meter (m3). A unit of volume is a cube whose side has a unit length (1cm, one dm, 1m, etc.), so it is measured in cubic units (cm ^ 3, dm ^ 3, m ^ 3, etc.). And is often expressed as liters.

## Common Volume Units

A **liter** is a unit of measurement for volume and it is only in use for fluids.

The volume in SI is a cubic meter, denoted by m3, defined by the volume of a cube whose edges are one meter long.

A **cubic meter** is a unit of measurement for volume in the International System of Units (SI). It is defined as the volume of a cube with a side length of 1m:

There are also old units of measurement that are still in use today, for example, the gallon. Therefore, only three-dimensional bodies have volume, while figures in one dimension (for example, a line) and two dimensions (for example, a square) have no volume. That is, it is equal to zero. We define in Mathematics volume using integral calculus, approximating the body as the sum of the volumes of a large number of tiny cubes.

A cube is a geometric body, one of Plato’s bodies. A cube belongs to parallelepipeds; it is a regular four-sided prism- it consists of six equal squares, its sides. It has 12 edges and eight tops.

## Other SI units for volume

The unit for volume is the cubic meter (m3), although smaller units (dm3, cm3, mm3) can also be in use in addition to this unit.

- 1 m3 = 1000 dm3
- 1 dm3 = 1000 cm3

In addition to these units, the following units are also often in use:

1 l (or L) = 1 dm3

1 ml = 1 cm3

## Volume formulas and how to calculate volume?

**Volume rectangle-based solids**

The formula for calculating the area of rectangular objects is length * width, and the basic formula for calculating volume is ** length * width * height**. If you need to calculate different dimensions, such as pool volume calculation, you can use depth instead of height, and the result will not change. When calculating three-dimensional objects, the most important thing is that you can multiply in any order, and the result will not change.

**The volume of Prisms and Cylinders**

This basic formula can also be extended to the volume of cylinders and prisms. Instead of a rectangular end, it has a different shape: a circle for a cylinder, a triangle, a hexagon, or any other polygon for a prism. For cylinders and prisms, the volume is effectively the area of one side multiplied by the depth or height of the shape. Therefore, the basic formula for the volume of prisms and cylinders is:

*Area of final shape × height/depth of prism/cylinder.*

**The volume of Cones and Pyramids**

The same principle as the previous one (width × length × height) is applied to the calculation of the volume of a cone or pyramid**,** except that because they reach a point, the volume is only a part of the total that would be if they were inside the same shape (cross-section**)** through. The **volume** of a **cone** or **pyramid** is exactly one-third the volume of a box or cylinder with the same base** **area. Therefore, the** **formula is:

*Area of basic or final shape × height of cone/pyramid × 1/3*

## Anglo-American units of measurement for volume

Anglo-American units are a set of very diverse individual units of measurement or units of incoherent systems. They originated in English-speaking countries; they have remained a tradition to this day. Due to their significant political and economic influence, they are still in use in international trade and information exchange. There are two groups of Anglo-American units:

English units or the imperial system of measures (so-called U.K. units) used in the United Kingdom, from where they spread to the former British colonies, and

U.S. units or the U.S. system of measures (so-called U.S. units), used in the U.S.

Anglo-American units differ in many respects from the so-called meter units (International System of Units). Larger and smaller units are formed in different ways; (sometimes with a ratio of 12; for example, inch or inch), they are inconsistent with each other, so many conversion factors or factors, units of the same name have different values in different countries and for different purposes (for example barrel), and conversely, units of the same value have different names in different countries (for example cental). U.K. units relied on their own primers (they only relied on meter units since 1963), and U.S. units were never systematically legal. In all these countries, Anglo-American units are gradually being replaced by S.I. units. The basic units of these systems are for foot length, for seconds, and for pound mass.

U.S. and British volume units include cubic inch (cu in), cubic foot (cu ft), cubic yard (cu yd), cubic mile (cu mi), teaspoon, tablespoon, ounce liquid (fl oz), dram liquid (fl dr), gill (gi), pint liquid (pt), quarter (quart) liquid (qt), gallon (gal), minim (min), barrel (bbl), pek (pk), bushel (bu), hogshead.

## Units of measurement

**Gallon**

Gallon (English gallon northern French gallon, Old French Jalon, perhaps from Celtic; designation gal) is an Anglo-American unit of volume used to express the volume of liquids. There are English gallons (U.K. gallons), valued at about 4,546 liters, and American gallons (U.S. gallons), valued at about 3,785 liters. Larger and smaller units are derived from U.K. gallons and only smaller units from U.S. gallons.

**Barrel**

Barrel (English barrel Latin articulus; mark bbl) is the name of many Anglo-American units of volume or mass, of different values, depending on the country, goods, and purpose. Bulk barrels range from 31 to 42 gallons (about 117 to 159 liters). The value by weight is very different. For example, a barrel of salt 127 kg, a barrel of flour 88.9 kg, a barrel of butter 101.6 kg. In international trade in oil and derivatives, an oil barrel (petroleum barrel) is in use, with a value of 42 U.S. gallons, i.e. approximately 159 liters.

**Pinta**

A pint is an old unit of volume. In the past, there were many different pints. The old Croatian or Zagreb pint was in use, which until 1733 was worth about 3,124 liters, then about 3,332 liters, the Hungarian pint, worth about 1,666 litres, and the Viennese pint (gauge, jug, Viennese). Eye), which from 1761 until the introduction of the Metric System the value was about 1,415 liters. A pint of liquid (pt) in the American system of measures is 473.176 5 ml. In the imperial system of measures about 568.2 ml.

**Bushel**

Bushel (bu) is an Anglo-American unit of dry matter volume, the value of British bu = 8 gallons = 36,368 72 liters, American bu = 2150.42 in³ = 35,239 070 160 88 liters.

## Volume calculators for several common shapes:

### Cylinder

V = \pi *r *2h### Cone

V = \frac{1}{3} * \pi * r^2### Cube

V = a * a * a### Rectangular prism (box)

V = length * width * height### Triangular prism

V = A *h**Where A is Area and h is height.**

### Pyramid

V = \frac{1}{3} * A * h**Where A is Area and h is height.**

### Capsule

V = \pi r^2 ((\frac{4}{3}) r+ a)**Where r is radius and a is area.**

### Hemisphere

V = \frac{2}{3} * \pi * r^3### Spherical cap

V = \frac{1}{3}* \pi * h^2 (3h – h)### Hollow cylinder / tube

V = \pi (R^2-r^2)h## Frequently Asked Questions

**How to find volume?**

**Wh ile** the basic formula for the area of

**rectangular shape is length × width, the basic formula for volume is length × width × height.**

****a**What is volume measured in?**

Volume is the measure of **th ree-dimensional** space

**that is occupied**by matter or enclosed by a surface, measured in cubic units.

**What is the difference between surface area and volume?**

The surface is a **two –dimensional** measure while volume is a

**three**measure. Two figures can have the same volume but different surfaces.

**–**dimensional**What is the volume of the Earth?**

The ** earth** has a volume of

**a**1,083,206,916,846 cubic kilometers (259,875,159,532 cubic miles). According to some astronomers, about 1.3 million Earths could fit in the sun.

**ppr**o**xima**t**ely****How to calculate the volume of a cylinder?**

V = A h.

Since the area of a circle = π r 2, then the formula for the volume of a cylinder is:

V = π r 2 h.

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