A prism is a three-dimensional shape in which two congruent two-dimensional shapes face each other and are connected together by the surfaces perpendicular to them. A prism is known as a

A parallelopiped is an example of an oblique prism having parallelogram bases.

Following figure demonstrates a hexagonal prism.

The prisms can have different shapes depending upon the shape of base. A triangular prism and a rectangular prism (also called cuboid) are shown in the diagrams below.

The prisms have following main properties -

In this article, we are going to learn about the concept of volume of a prism. We shall understand the definition and formula of the volume of prism as well as see examples based on this.

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The volume of a prism is eventually a measurement of the units occupied by the prism. It is also defined as the number of units used to fill a prism. The volume of prism is the product of base area and height.

The volume of a Prism is represented by cubic units or unit$^{3}$ like cubic centimeter (cm$^{3}$), cubic millimeter (mm$^{3}$) and so on. Volume of prism is the product of base area and height.

**For Triangular Prism:**

Equation for volume of a prism is, V = $\frac{1}{2}$bh H

where, b = Side of base, h = Height of base and H = Height of prism

For Square Prism:

Equation for volume of square prism is, V = (Side)$^2$ H

where, Area of base = (Side)$^2$ and H = Height of prism

### Solved Examples

**Question 1: **

** Solution: **

**Question 2: **A metallic sheet is of the rectangular shape with dimensions 48 cm x 36 cm. From each one of its corners, a square of 8 cm is cutoff. An open box is made of the remaining sheet. Find the volume of the box.

** Solution: **

The volume of a Prism is represented by cubic units or unit$^{3}$ like cubic centimeter (cm$^{3}$), cubic millimeter (mm$^{3}$) and so on. Volume of prism is the product of base area and height.

Volume of a solid object is the measure of the space occupied by it. Volume of a prism in general is the area of the base times the height between the two bases. The formula for volume of a prism is as follows:

**Volume of prism = Area of Base $\times$ Height of Prism**

Equation for volume of a prism is, V = $\frac{1}{2}$bh H

where, b = Side of base, h = Height of base and H = Height of prism

For Square Prism:

Equation for volume of square prism is, V = (Side)$^2$ H

where, Area of base = (Side)$^2$ and H = Height of prism

Given below are some of the examples to find the volume of a prism.

Find the volume of a triangular prism with dimensions 12 m, 16 m and 20 m as shown in figure.

The equation for calculating the volume of a triangular prism is V = Area of base $\times$ Height of Prism

Since base is triangular.

Area of triangle = $\frac{1}{2}$ $\times$ base $\times$ height

= $\frac{1}{2}$ $\times$ 12 $\times$ 16 = 96

Now, Volume of prism = 96 $\times$ 20 = 1920 cubic meter

To make an open box, a square of side 8 cm is cut off from each of the four corners and the flaps are folded up.

The dimensions of the box are

Length = 48 - 8 - 8 = 32 cm

Width = 36 - 8 - 8 = 20 cm

Height = 8 cm

Volume of box = B $\times$ h

where, B = area of rectangular base = length $\times$ width = 32 $\times$ 20

Volume of the box = Area of base $\times$ height

= 32 $\times$ 20 $\times$ 8 = 5120

$\therefore$ Volume of the given box is 5120 cubic cm.

Practice with the following problems.

**Problem 1 :** Find the volume of a triangular prism whose base is a right triangle with perpendicular sides measuring 5 cm and 10 cm. The height of this prism being 16 cm.

**Problem 2 :** Calculate the volume of a prism whose area of base 72 square meter and height is 5 meter.

**Problem 3 :** Determine the volume of a hexagonal prism with a regular hexagon base of side 10 centimeter and height 24 cm.

**Hint :** The hexagon is composed of six equilateral triangles. Therefore, we can find the area of hexagonal base by using formula of area of equilateral triangle (side 10 cm) and then multiplying it by 6.

More topics in Volume of a Prism | |

Volume of a Trapezoidal Prism | Volume of a Triangular Prism |

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