Guide to Understanding How to Calculate the Volume of a Prism

A Guide to Understanding How to Calculate the Volume of a Prism

• An Introduction to Volume of a Prism

The volume of a prism is referred to as the total space occupied by a prism. This will reveal how to calculate prism volume in easy steps. However, before we get into that part, let's discuss what actually a prism is. We all know that prism is a 3D solid object with both the volume and subject area. It is basically a solid geometric figure with two identical flat faces, ends, and the same cross-section all along its length.

Prisms are named on the basis of the shapes of their cross-section. For instance, a prism with a triangular cross-section is a triangular prism, while a prism with a rectangle is a rectangular prism, and so on.

Here are the types of prisms:

• Square prism
• Triangular prism
• Pentagonal prism
• Cuboid or rectangular prism
• Hexagonal prism

Chat Now

How to Calculate the Volume of Prism?

You will require knowing the height and area of a prism to find the volume of the prism. All you require to do is calculate the area of its base and then multiply it by its height. The volume of the prism is also measured in cubic units, i.e., cubic centimetres, cubic meters, etc.

The general volume of the volume of a prism is:

Volume of a prism = Base Area x Length

Calculating the Volume of a Triangular Prism

A prism with 3 rectangular faces and 2 parallel bases is a triangular prism. The triangular bases are joined by lateral faces and are parallel to each other. The space occupied by the triangular prism is referred to as the volume of the triangular prism. These are the steps for calculating the triangular prism:

1. Write the formula for the triangular prism

V= ½ x length x width x height.

2. Find the area of the base face

So to calculate the volume of a triangular prism, you will need to find the area of the triangular base. You can find the base of the prism by multiplying ½ times the base and height of the triangle.

a = Length of the triangular prism

b= base length of a triangular prism

h= height of a triangular prism

Calculating the Volume of a Cube

The volume of a cube refers to the total cubic units occupied by it. A cube comes with six faces, twelve edges and eight verticals. The unit volume of the cube is in cubic units such as centimeters³, inches³, feet³, meters^3. As all the faces of the cube are square in shape, the length of the edges is equal. Thus, the cube's length, height, and width are of equal length.

Hence, the volume of the cube = a x a x a

Unlock More Tips

Calculating the Volume of a Rectangular Prism

The volume of a rectangular prism refers to the space occupied by the rectangular prism. It is a polyhedron with two pairs of congruent and parallel bases. It consists of 12 sides, 6 faces and 8 verticals.

Steps to be followed to find the volume of a rectangular prism:

• Find the length of the rectangular prism
• Find the width of the rectangular prism
• Find the height of the rectangular prism
• Multiply the length, width and height to find the volume of the rectangular prism.

Volume = Length * Height * Width

Check More Benefits

Calculating the Volume of a Trapezoidal Prism

A trapezoidal prism is a three-dimensional shape with two trapezoidal bases and four parallelogram faces. Trapezoidal prism comes with 12 edges, 6 faces and 8 vertices.  The base of a trapezoid prism is trapezium/trapezoid.

So to find the volume of a trapezoid prism, follow the steps below:

• Find the area of the base (area of the trapezoid)

½ (b₁ + b₂) x h

• Calculate the volume of a prism formula using the volume of a prism

The volume of trapezoid prism – the area of base x length

= ½ (b₁ + b₂) x h x L

Calculating the Volume of a Regular Pentagonal Prism

A pentagonal prism is a type of prism that comes with two pentagonal bases and five rectangular sides. The regular right pentagonal prism is known as a uniform polyhedron. Here is how you should calculate the volume of a regular pentagonal pyramid.

Volume of pentagonal prism = (5/2) x a x b x h

SUMMING UP,

Learning how to calculate the volume of a prism is a crucial part of mathematics. However, often students find this to be the most overwhelming task. Read on the find simpler steps to calculate the volume of a prism, rectangular prism, triangular prism, cube, etc.

Click For Guidance

Most Popular Questions Searched By Students:

Q. How to Find the Volume of Prism?

Answer: The volume of the prism can be found by obtaining the product of the base area and height of the prism. Here is the formula = V- B x H

Q. What is the volume?

Answer: Volume refers to the total amount of space existing in a certain 3D object. A scalar quantity expresses the amount of three-dimensional space enclosed by a closed space.

Q. What is a prism, and what distinguishes between a right prism and an oblique prism?

Answer: Prism is a type of three-dimensional shape with two identical shapes facing each other and a uniform cross-section along its length.

Lateral sides in a right prism are perpendicular to the bases. Hence, all of them are rectangular. On the other hand, the lateral sides in the oblique prism are not perpendicular to the bases. Hence some of them are non-rectangular parallelograms. The side faces in the right prism are rectangles, whereas the side faces in an oblique prism are parallelograms.

Q. How to label the parts of a prism and how to distinguish between an oblique and a right prism?

Answer:  A prism consists of two identical ends, flat faces and a uniform cross-section across its length.

Q. Word problems about the volume of prisms

Answer: Here is an example of calculating the volume of a prism:

Find the volume of a prism whose base area is 4 square inches and height is 8 inches.

Solution: We already know that the volume of the prism is V+ B X H

B = 4 square inches

H= 8 inches

Thus V = 4 x 8 = 32

Therefore, the volume of the prism is 32 in³

Q. How do you find the base area of prism if the volume is given?

Answer: Suppose the volume of the prism is 27, and the height is given 7 inches. So how do you find the base area of the prism?

Following the formula of volume of prism V= B x H

Thus, Base area of the Prism = V/H = 27/7 = 3

Q. How Does the Volume of Prism Change if the Type of Prism Changes?

Answer:  Since the volume of the prism depends on the prism's base area, the prism, the base of the prism, changes with the change type of prism. Such change in the base area brings changes in the volume of the prism.

Tell Us What You Need