# Volume Formulas

## Volume Formulas

The amount of three-dimensional space that an object or shape takes up is known as its volume. It is typically expressed in cubic units. In other words, the volume of any object or container refers to the amount of liquid (gas or liquid) it can hold. Arithmetic formulas can be used to quickly compute the volume of three-dimensional mathematical forms, including cubes, cuboids, cylinders, prisms, and cones, among others. On the other hand, one can use integral calculus to determine the volumes of complex shapes.

## What is Volume Formula?

A mathematical phrase called the Volume Formulas is used to calculate how much space (or vacuum) each three-dimensional object takes up overall.

An object’s Volume Formulas is used to determine the total cubic capacity that it can store. Units of volume, or cubic units, are used to indicate a 3-dimensional shape’s volume unit.

### Volume Formulas of 3-D Shapes

The Volume Formulas are now known to be used to compute the volume of a three-dimensional object. This part will teach us how to calculate the volumes of various 3-D shapes using their corresponding dimensions.

### Volume Formula of Cube

When all three sides of a cube are equal in size, the Volume Formulas for a cube depend on those three sides. The area that a cube occupies is known as its volume. The following is the general formula for a cube’s volume:

A cube’s volume is equal to a, a, and a3 cubic units, where an is the cube’s side length.

The Volume Formulas of a cube using the diagonal is V = (3d3)/9, where d is the cube’s diagonal length.

### Volume Formula of Cuboid

The volume of a cuboid formula is used to determine the volume of space that the cuboid encloses. Mathematically, a cuboid’s volume can be calculated using the following generic formula:

Cuboid volume is equal to the base area times the height in cubic units.

The cuboid’s base area is equal to l b square units.

Thus, the volume of a cuboid is given by V = l b h = lbh units3, where l b h are the cuboid’s length, breadth, and height.

### Volume Formula of Cone

The volume formula for a cone is used to determine how much space is occupied within a 3-D-shaped cone with a circular base and a height and radius of r and h, respectively. The cone’s general volume formula is as follows:

A cone’s volume is equal to (1/3)r2h cubic units.

Here,

The cone’s base (circle) has a radius of “r.”

The constant ‘h’, which represents the cone’s height, has a value of either 22/7

### Volume Formula of Cylinder

The quantity of space (or capacity) occupied inside the cylinder is calculated using the cylinder’s volume formula. A circle serves as the right circular cylinder’s base, and an r-radius circle has a r2-radius area. Consequently, the formula for a cylinder’s volume is

A cylinder’s volume is equal to r2h cubic units.

Here,

The cylinder’s base (circle) has a radius of “r.”

H stands for the cylinder’s height.

The value of the constant is either 22/7 (or) 3.142.

Thus, a cylinder’s volume is directly related to both its height and the square of its radius. In other words, if the cylinder’s radius doubles, its volume will increase by a factor of four.

### Volume Formula of Sphere

A wonderful illustration of a form that resembles a sphere is a football. It has a circular structure and is a solid object in three dimensions. The volume of a sphere or ball is defined as the volume of air that fills it. The following is the sphere’s volume formula:

The sphere’s volume is (2/3)r2h.

If the sphere’s diameter equals 2r

Therefore, the sphere’s volume is equal to (2/3)r2h = (2/3)r2(2r) = (4/3)r3 cubic units.

A sphere has a volume of (4/3)r3 cubic units.

Here,

The sphere’s height (h) and radius (r) are both constants with values of either 3.142 or 22/7.

### Volume Formula of Hemisphere

Since a hemisphere is half of a sphere, calculate its volume using the sphere’s volume formula. Now take into account that a sphere has a radius of ‘r’ units and a volume of (4/3)r3.

As a result, the formula for the hemisphere’s volume is: V = ½ (4/3)πr3

Hemisphere’s volume is equal to (2/3)r3 cubic units.

Here,

The hemisphere’s radius, or “r,” has a constant value of either 3.142 or 22/7.

### Volume Formula of Prism

The product of the base’s area and the prism’s height provides the volume formula for prisms. It is written mathematically as:

Prism volume is given by V = B h units3.

Here,

Base area in square units is “B.”

The prism’s height is expressed in units as “h.”

Based on how the bases of prisms are shaped, there are seven different varieties of prisms. The various prism bases have an impact on the volume formula for prisms. To get the idea behind the volume formulas for various prisms, look at the volume of prisms.

### Volume Formula of Pyramid

A pyramid’s volume is equivalent to one-third of a prism’s volume (i.e., their bases and heights are congruent). Thus,

The pyramid’s volume (V) equals 13 (Bh) units3, where

B is the pyramid’s base area measured in square units.

h is the pyramid’s height in units of altitude.

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