Geometry: Geometry: Geometry Explained: Volume of a Prism

Understanding Prism Volume 📐

The volume of a prism is the measure of the space it occupies. To calculate it, you need to understand the prism's base area and its height. The general formula is:

Volume = Base Area × Height

Types of Prisms and Their Volume Calculation 🧊

• Right Prism: Sides are perpendicular to the bases.
• Oblique Prism: Sides are not perpendicular to the bases.

The shape of the base determines how you calculate the 'Base Area'. Here are a few common examples:

1. Rectangular Prism: Base is a rectangle. Area = length × width.
2. Triangular Prism: Base is a triangle. Area = 1/2 × base × height.
3. Cylindrical Prism: Base is a circle. Area = πr², where r is the radius.

Calculating Volume: Examples ✍️

Example 1: Rectangular Prism

A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 4 cm. Calculate its volume.

length = 5
width = 3
height = 4

base_area = length * width
volume = base_area * height

print(volume)
# Output: 60

The volume is 60 cm³.

Example 2: Triangular Prism

A triangular prism has a base triangle with a base of 6 cm, a height of 4 cm, and the prism's height is 8 cm. Find the volume.

base_triangle_base = 6
base_triangle_height = 4
prism_height = 8

base_area = 0.5 * base_triangle_base * base_triangle_height
volume = base_area * prism_height

print(volume)
# Output: 96

The volume is 96 cm³.

Example 3: Cylindrical Prism (Cylinder) 🛢️

A cylinder has a radius of 3 cm and a height of 7 cm. Calculate its volume.

import math

radius = 3
height = 7

base_area = math.pi * radius**2
volume = base_area * height

print(volume)
# Output: 197.92033717615698

The volume is approximately 197.92 cm³.