A crucial component of geometry is understanding the volume of prisms. A three-dimensional geometry having two identical parallel ends is called a prism. The prism’s volume shows how much room it occupies. Despite the fact that prisms can be classified into rectangles, triangles, etc., the overall idea stays the same: to find the area of the base and multiply it by the height.
This tutorial gives you the wasteland formula so that you will calculate volumes of different shapes.
What Is a Prism?
Prism is a three dimensional geometric shape which has two parallel bases of similar shapes. The bases may be of various shapes such as rectangles, triangles, pentagons or hexagons.The surfaces joining the bases are called lateral surfaces. Prism is named based on its base.
Types of Prisms
For example, some common types of prisms are:
- Rectangular prism
- Triangular prism
- Pentagonal prism
- Hexagonal prism
- Square prism
An example of prism is a rectangular box in case of rectangular prism while triangular prism resembles a tent shape.
What Is the Volume of a Prism?
The prism’s volume refers to the amount of three-dimensional area measured within a prism. Volume is measured in cubic units such as m³, cm³, or in³.
The basic equation is as follows: Volume = Area of Base × Height
In mathematical terms;
V = B × h
Where;
- V = volume of the prism
- B = area of base
- h = prism’s height
The most crucial thing to remember is to find out the area of base in the beginning of the calculation of volume.
The prism volume formula is:
V = B × h
This formula doesn’t work for certain kinds of prisms.
For instance, if the base area of the prism is 20 cm² and height is 8 cm, then:
V = 20 × 8;
V = 160 cm³
Hence, the volume of the prism is equal to 160 cm³.
Remember that volume uses cubic units because it measures three-dimensional space.
How to Find the Volume of Prisms Step by Step
The calculation of the volume of prisms will become simpler when following three easy steps.
Step 1: Finding the Shape of the Base
Initially, find out the shape of the base of the prism. The base may take a rectangle, triangle, pentagon, or any other form.
Step 2: Calculate the Area of the Base
Apply the area formula relevant to the particular base.
For instance:
Rectangle: A = l x w
Triangle: A = ½ × b × h
Step 3: Multiply the Area of the Base by the Height of the Prism
After finding the area of the base, multiply it by the height/length of the prism: V = B × h
Keep in mind that the units should match.
Recommended Reading: How to Round to the Nearest Hundredth: Simple Steps, Rules & Examples
Volume of Rectangular Prisms
Rectangular prism volume is one of the easiest applications of the prism volume formula. A rectangular prism is a solid whose base is a rectangle. In this case, the base area is:
Base Area = Length × Width
The volume formula will be:
V = Length × Width × Height
Example: Volume of a Rectangular Prism
Consider that a rectangular prism has the following measurements:
- Length = 8 cm
- Width = 5 cm
- Height = 3 cm
In this case, we shall start by multiplying the three measures together:
V = 8 × 5 × 3
V = 120 cm³
Thus, the volume is 120 cubic centimeters.
Another Example :
A storage box has a length of 10 inches, width of 4 inches, and height of 6 inches.
V = 10 × 4 × 6
V = 240 in³
This means the box can contain 240 cubic inches.
How to Find the Volume of a Triangular Prism
For a triangular prism, you first need to find the area of the triangular base.
The area of a triangle is:
Area = ½ × base × triangle height
Then multiply that area by the length or height of the prism.
Example:
A triangular prism has:
- Triangle base = 6 cm
- Triangle height = 4 cm
- Prism length = 10 cm
First, find the triangular base area:
B = ½ × 6 × 4
B = 12 cm²
Now calculate the volume:
V = 12 × 10
V = 120 cm³
Reco
Volume of Different Types of Prisms
Volume of Different Types of Prisms
The same basic formula can be used to calculate the volume of different types of prisms. First, find the area of the prism's base, then multiply it by the prism's height.
| Type of Prism | Base Area | Volume Formula |
|---|---|---|
| Rectangular Prism | Length × Width | L × W × H |
| Triangular Prism | ½ × Base × Triangle Height | Base Area × Prism Height |
| Pentagonal Prism | Area of Pentagon | Base Area × Prism Height |
| Hexagonal Prism | Area of Hexagon | Base Area × Prism Height |
Key formula: Volume of a prism = Base Area × Prism Height.
Volume of Prisms and Cylinders
The volume of prisms and cylinders is often taught together because both shapes use a similar volume concept.
For a prism:
V = B × h
For a cylinder:
V = πr²h
In both formulas, the area of the base is multiplied by the height.
A prism has a polygon-shaped base, while a cylinder has a circular base.
Conclusion
Determining the volume of prisms can be achieved through one fundamental concept: determine the base area of the prism and multiply it by its height.
The general formula for volume of a prism is:
V = B × h
To solve for volume of a rectangular prism, use:
V = length × width × height
While for the volume of a triangular prism, first solve for the triangular base area before multiplying by the length of the prism. Same principle applies when determining the comparison of volumes of prisms and cylinders.
If the right base is correctly identified along with its area formula, prism volume becomes a lot easier.
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