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# Volume of a Prism

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 right prism when the joining edges and bases are exactly perpendicular. This is possible when joining faces are rectangular in shape. When bases are not perpendicular to the joining edges, such prism is called an oblique prism.

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 -
(i) They have identical ends.
(ii) They are made up of flat faces.
(iii) They have identical cross section allover along their length.

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.

 Related Calculators Calculate Volume of a Triangular Prism Calculate Volume of Rectangular Prism Prism Volume Calculator Prism Surface Area Calculator

## Definition

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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.

## Volume of a Prism Formula

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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

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

## Find the Volume of a Prism

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

### Solved Examples

Question 1:

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

Solution:

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

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:

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 Problems

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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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