VOLUME OF PRISM

The prism is a type of polyhedron with all of its faces which is flat and all of its bases are parallel to one another.  The prism has the surface area and volume because the prism is a three-dimensional structure. The volume of a prism, as well as its formulas, will be discussed.

VOLUME OF PRISM

The capacity of a prism is determined by its volume. Prisms come in a variety of shapes and sizes, including triangular, square, rectangular, pentagonal, hexagonal, and octagonal prisms. However, regardless of the type of prism, the procedure for writing the volume formula of any prism stays the same. In either instance, the principle of formulating the formula for the prism’s volume remains the same.

Definition of volume of prism

A prism’s volume is defined as the amount of space it takes up. A prism is a solid three-dimensional structure with two identical faces and other faces that look like a parallelogram. The varying shapes of the bases influence the naming tradition of this polyhedron. Every prism has a unique base, such as a triangular prism (triangular base), a square prism (square base), a rectangular prism (rectangular base), a pentagonal prism (pentagonal base), a hexagonal prism (hexagonal base), or an octagonal prism (octagonal base) (octagonal base).

Because each prism is a three-dimensional shape, its volume is also three-dimensional. A prism’s volume is measured in cubic metres, cubic millimetres, cubic inches, or cubic feet, among other units.

Formula for volume of prism 

Let us now look at the volume formulas for various prisms, such as the volume of a triangular prism, rectangular prism, pentagonal prism, and so on.

The product of the area of the base and the height of the prism gives the volume of the prism.

Volume of prism = base area × height

As the bases of various types of prisms vary, so do the formulas for calculating the prism’s volume.

TRIANGULAR PRISM : –

A prism with three rectangular faces and two triangular bases is known as a triangular prism. Because the triangular prism’s cross-section is a triangle.

Volume of triangular prism :- base area × height

                                                  = ½ × b × a × h

Where a , b are the base width and length of the triangular prism and h is the height of the prism.

RECTANGULAR PRISM

Four rectangular faces and two parallel rectangular bases make up a rectangular prism. A rectangular prism’s cross-section is known to be a rectangle.

Volume of rectangular prism :- base area × height

                                                  =  b × a × h

Where a , b are the base width and length of the rectangular prism and h is the height of the prism.

PENTAGONAL PRISM :

Five rectangular sides and two parallel pentagonal bases make up a pentagonal prism.

Volume of pentagonal prism :- base area × height

                                                  = ⁵/2 × b × a × h

Where a , b are the base width and apothem length of the pentagonal prism and h is the height of the prism.

HEXAGONAL PRISM :-

A hexagonal prism is a prism with six rectangular sides and two hexagonal bases that are parallel to each other. The hexagonal prism’s base area is 3ab.

Volume of hexagonal prism :- base area × height

                                                  = 3 × a × b × h

Where a , b are the base width and apothem length of the hexagonal prism and h is the height of the prism.

STEPS TO CALCULATE THE VOLUME OF PRISM :-

Here are the following steps which is used to determining the prism’s volume:

Step 1:  list the dimensions of the prism .

Step 2: Use the formula Volume = Base area × Height to calculate the volume of the prism .

Step 3: when we know the value of the prism’s volume has been determined, add the unit of prism volume at the end (in terms of cubic units).

CONCLUSION :-

A prism is a polyhedron made up of an n-sided polygon base, a second base that is a translated copy (moved rigidly without rotation) of the first, and n additional faces, all of which must be parallelograms, that connect the two bases. Translations of the bases are all cross-sections parallel to the bases.

Every prism has a unique base, such as a triangular prism (triangular base), a square prism (square base), a rectangular prism (rectangular base), a pentagonal prism (pentagonal base), a hexagonal prism (hexagonal base), or an octagonal prism (octagonal base) (octagonal base).