Pyramid Volume Calculator
Calculate the volume of a pyramid with our pyramid volume calculator using base area and height. Get accurate results with the pyramid volume formula.
m
m
Pyramid Volume
120m³
Decimals:
Step-by-Step Mathematical Solution
Formula:V = (1/3) × Base Area × Height
Steps:
1.Base Length (l) = 6 m, Base Width (w) = 6 m, Height (h) = 10 m
2.Formula: V = (1/3) × Base Area × Height
3.Calculate Base Area (B): B = 6 × 6 = 36 m²
4.Multiply Base Area by Height: B × h = 36 × 10 = 360
5.Divide by 3: V = 120 m³
Calculated Volume:120 m³
What Is a Pyramid?
A pyramid is a polyhedron formed by connecting a polygonal base to a single apex point. Common pyramids have square or rectangular bases.
Volume of a Pyramid Formula
Standard Formula
V = (1/3) × Base Area × Height
Formula Variables Explained:
lBase Length
Length of the pyramid base.
wBase Width
Width of the pyramid base.
hHeight
Perpendicular distance from base to peak vertex.
The volume of any pyramid is one-third of the volume of a prism with the same base and height: V = (1/3) × Base Area × Height.
How to find the volume of a Pyramid?
- 1Calculate base area B = length × width.
- 2Multiply base area B by height h.
- 3Divide by 3.
Example: Calculate the Volume of a Pyramid
Example 1: Volume of a square pyramid
Problem: A pyramid has a square base with sides 6 m and height 10 m.
Solution Steps:
- Base Area = 6 × 6 = 36 m²
- V = (1/3) × 36 × 10 = 120 m³
Final Volume:120 m³
Frequently Asked Questions (FAQ)
Q: Why is pyramid volume 1/3 of a prism?
A rectangular prism can be divided into three identical pyramidal solids sharing the same base area and height.