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Volume of a Cylinder

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Volume of a Cylinder

Study Guide

Key Definition

The volume of a cylinder is calculated using the formula $V = \pi r^2 h$, where $V$ is the volume, $r$ is the radius of the base, and $h$ is the height.

Important Notes

The base of the cylinder is a circle with area $\pi r^2$
Height $h$ is the perpendicular distance between the base and top
Volume is measured in cubic units
Use $\pi \approx 3.14159$ for calculations
Ensure all measurements are in the same unit

Mathematical Notation

$\pi$ represents the constant pi, approximately 3.14159

$r$ is the radius of the base circle

$h$ is the height of the cylinder

$\times$ represents multiplication

Remember to use proper notation when solving problems

Why It Works

The volume formula $V = \pi r^2 h$ works because it calculates the area of the base circle and multiplies it by the height to fill the space inside the cylinder.

Remember

Always square the radius first before multiplying by $\pi$ and the height.

Quick Reference

Volume Formula:$V = \pi r^2 h$

Understanding Volume of a Cylinder

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Video explanation of this concept

Beginner

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Beginner Explanation

The volume of a cylinder is found by taking the area of its circular base and multiplying by its height. Since the base area is $\pi r^2$, the formula is $V = \pi r^2 h$. This gives the space inside the cylinder in cubic units.

Practice Problems

Test your understanding with practice problems

Quick Quiz

Single Choice Quiz

Beginner

If a cylinder has a radius of $3$ units and a height of $5$ units, what is its volume?

Real-World Problem

Question Exercise

Intermediate

Teenager Scenario

Imagine a can of soda has a radius of $2.5$ cm and a height of $12$ cm. Calculate its volume.

Thinking Challenge

Thinking Exercise

Intermediate

Think About This

Given a cylinder with a volume of $100\pi$ cubic units and a height of $4$ units, find its radius.

Challenge Quiz

Single Choice Quiz

Advanced

A cylinder has a base area of $25\pi$ square units and a height of $10$ units. What is its volume?

Recap

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Review key concepts and takeaways