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Volume of a Pyramid

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Volume of a Pyramid

Study Guide

Key Definition

The volume $V$ of a pyramid is given by $V = \frac{1}{3}Bh$, where $B$ is the area of the base and $h$ is the height.

Important Notes

The base $B$ can be any polygon.
Ensure all measurements are in the same unit before calculating volume.
Volume is measured in cubic units like $cm^3$ or $m^3$.
A pyramid has one base and triangular faces.
The height $h$ is the perpendicular distance from the base to the apex.

Mathematical Notation

$\frac{1}{3}$ means one-third

$+$ represents addition

$-$ represents subtraction

$\times$ or $*$ represents multiplication

$\div$ or $/$ represents division

Remember to use proper notation when solving problems

Why It Works

The formula $V = \frac{1}{3}Bh$ works because it accounts for the tapering shape of the pyramid, which occupies one-third of the space compared to a prism with the same base and height.

Remember

Always calculate the base area $B$ accurately, and ensure height $h$ is perpendicular to the base.

Quick Reference

Volume Formula:$V = \frac{1}{3}Bh$

Understanding Volume of a Pyramid

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Video explanation of this concept

Beginner

Start here! Easy to understand

Beginner Explanation

To find the volume of a pyramid, calculate the area of the base B (for a triangle use $\tfrac{1}{2}bh$ or for a rectangle use $l\times w$). Then multiply B by the pyramid’s height h and divide by 3 using the formula $V=\frac{1}{3}Bh$.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

What is the volume of a pyramid with a base area of $100\,cm^2$ and height $18\,cm$?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine you need to build a tent that is shaped like a pyramid with a square base of side $5\,m$ and a height of $3\,m$. What is the volume of the tent?

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

If a pyramid's volume is $48\,cm^3$ and its base area is $24\,cm^2$, what is its height?

Challenge Quiz

Single Choice Quiz

Advanced

If the base of a pyramid is a triangle with area $30\,m^2$ and the height is $12\,m$, what is the volume?

Recap

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Review key concepts and takeaways