The formula for the volume of a prism is V = B × h.
Understanding the Prism Volume Formula
According to the definition, the volume of a prism is calculated by multiplying the area of its base by its height.
- V represents the Volume of the prism.
- B represents the Area of the Base of the prism.
- h represents the Height of the prism (the perpendicular distance between the two identical bases).
This fundamental formula, Prism volume (V) = B × h, applies to all types of prisms, regardless of the shape of their base (e.g., triangular prism, pentagonal prism, etc.). The key is correctly calculating the area of the specific base shape.
Special Case: Rectangular Prisms
For a rectangular prism, the base is a rectangle. The area of a rectangle is calculated by multiplying its length and width.
The provided reference specifically notes that for a rectangular prism, the formula becomes:
- V = l × w × h
Here:
- l is the length of the base.
- w is the width of the base.
- h is the height of the prism.
In this case, the 'B' (Area of the Base) from the general formula V = B × h is simply l × w.
Applying the Formula
To find the volume of any prism, follow these steps:
- Identify the shape of the base.
- Calculate the area of the base (B). Use the appropriate formula for that specific shape (e.g., area of a triangle, area of a square, area of a circle if it were a cylinder, etc.).
- Measure or identify the height (h) of the prism.
- Multiply the base area (B) by the height (h): V = B × h.
Example
Let's calculate the volume of a rectangular prism with a base length of 5 cm, a base width of 3 cm, and a height of 10 cm.
- Shape of the base: Rectangle
- Area of the base (B): l × w = 5 cm × 3 cm = 15 cm²
- Height (h): 10 cm
- Volume (V): B × h = 15 cm² × 10 cm = 150 cm³
Alternatively, using the specific formula for a rectangular prism:
- Volume (V): l × w × h = 5 cm × 3 cm × 10 cm = 150 cm³
The unit for volume is always cubic units (e.g., cm³, m³, in³).
Understanding the base formula V = B × h allows you to calculate the volume of any prism, as long as you know how to find the area of its base.
