How to Find the Volume of a Prism? Volume of a Prism Formulas

How to Find the Volume of a Prism?

To find the volume of a prism, you need to follow a few simple steps. First, identify the dimensions of the prism. This includes knowing the area of the base and the height of the prism. The base of the prism can have different shapes, such as a triangle, square, rectangle, pentagon, hexagon, or octagon. The shape of the base doesn't change the method of finding the volume; it only affects the calculation of the base area.

Once you have the area of the base, the next step is to use the formula for the volume of a prism, which is V=B×H.

Here,

V stands for the volume,

B is the area of the base, and

H is the height of the prism. Multiply the base area by the height to get the volume.

After calculating the volume, ensure you add the correct unit of measurement, such as cubic meters, cubic centimeters, cubic inches, or cubic feet, depending on the dimensions given. Finding the volume of a prism involves measuring the base area and the height, using the volume formula, and then applying the correct unit of measure to your final answer.

Volume of a Prism Formulas

The formula for the volume of a prism is simple and applies to all types of prisms. It is given by the product of the area of the base and the height of the prism.

This formula can be written as V=B×H, where

• V is the volume,
• B is the base area, and
• H is the height of the prism.

Triangular Prism:

The base of a triangular prism is a triangle. To find the volume, you first calculate the area of the triangular base and then multiply it by the height of the prism. The formula is

Volume=Area of triangle×Height.

Square Prism:

A square prism has a square base. To get the volume, find the area of the square base and multiply it by the prism's height. The formula is

Volume=Area of square×Height.

Rectangular Prism:

For a rectangular prism, the base is a rectangle. You need to determine the area of the rectangular base and then multiply it by the height of the prism. The formula is

Volume=Area of rectangle×Height.

Trapezoidal Prism:

This prism has a trapezoid as its base. Calculate the area of the trapezoidal base and multiply by the height of the prism. The formula is

Volume=Area of trapezoid×Height.

Pentagonal Prism:

The base of a pentagonal prism is a pentagon. Find the area of the pentagonal base and multiply it by the height of the prism. The formula is

Volume=Area of pentagon×Height.

Hexagonal Prism:

For a hexagonal prism, the base is a hexagon. Calculate the area of the hexagonal base and multiply it by the height. The formula is

Volume=Area of hexagon×Height.

Octagonal Prism:

This type of prism has an octagonal base. Find the area of the octagonal base and multiply it by the height of the prism. The formula is

Volume=Area of octagon×Height.

Examples of Volume of a Prism

Let's explore more examples to understand how to calculate the volume of prisms using the formula

V=B×H, where

V is the volume,

B is the base area, and

H is the height.

Example 1: Rectangular Prism

Base: Rectangle with length 6 cm and width 4 cm

Solution:

Calculate the area of the rectangle base

Area=Length×Width=6×4 = 24 square centimeters

Now, apply the formula for volume:

V=Area×Height=24×8

V=192 cubic centimeters

Example 2: Square Prism

Base: Square with side length 5 cm

Height: 10 cm

Solution:

Calculate the area of the square base:

Area=Side×Side=5×5

Area=25 square centimeters

Now, apply the formula for volume:

V=Area×Height=25×10

V=250 cubic centimeters