Volume of a Cylinder

Statement

The volume of a cylinder is given by:

\[ V = \pi r^2 h \]

where \(r\) is the radius of the circular base and \(h\) is the perpendicular height.

Why it’s true

• Volume = base area × height.
• The base of a cylinder is a circle, with area = \(\pi r^2\).
• So, volume = \(\pi r^2 h\).

Recipe (how to use it)

1. Find the radius of the circular base.
2. Square it: \(r^2\).
3. Multiply by \(\pi\).
4. Multiply by height \(h\).
5. Answer in cubic units.

Spotting it

Look for 3D “tube” shapes — circular cross-section, same size along the height.

Common pairings

• Surface area of a cylinder.
• Unit conversions (litres ↔ cm³ ↔ m³).

Mini examples

1. Given: \(r=3\), \(h=10\). Find: Volume. Answer: \(90\pi\).
2. Given: \(r=7\), \(h=4\). Find: Volume. Answer: \(196\pi\).

Pitfalls

• Using diameter instead of radius (remember: radius = half of diameter).
• Forgetting to square the radius.
• Confusing surface area with volume.

Exam strategy

• Write the formula before substituting numbers.
• Check if height given is perpendicular, not slant.
• Leave answers in terms of \(\pi\) unless decimals are required.

Summary

The volume of a cylinder is the product of its base area and its height: \(V=\pi r^2 h\). Always check whether you’re given diameter or radius, and cube your units.