Can a percentage be greater than 100%?

Yes. Whenever a fraction is "improper" (the numerator is larger than the denominator), its value is greater than 1, and the resulting percentage will be over 100%. For example, 5/4 is equal to 125%.

Why do you multiply by 100?

The word "percent" comes from the Latin "per centum," which means "per hundred." When you convert a decimal (like 0.75) to a percentage, you are finding out how many parts it represents out of one hundred.

How do you convert a percentage back to a fraction?

To convert a percentage back to a fraction, write the percentage as a fraction with a denominator of 100, then simplify it. For example, 75% becomes 75/100, which simplifies to 3/4.

Cylinder Volume Calculator

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Hollow

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Radius

Height (h)

Volume

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r

Learn the Formula

Explore the mathematical foundation of the calculator, presenting the formula in multiple formats and explaining the principles behind it.

Core Formula: Solid Cylinder

Mathematical Notation

V = πr²h

Plain English

Volume equals Pi (π) times the radius (r) squared, multiplied by the height (h).

Justification: Cavalieri's Principle

The formula $V = \pi r^2 h$ is universally applicable to both right (straight) and oblique (slanted) cylinders. This is due to Cavalieri's principle, which states that if two solids have the same height and their cross-sectional areas at every level are equal, they have the same volume. Since a slanted cylinder is just a "pushed over" stack of the same circular discs that make up a right cylinder, its volume remains unchanged as long as the perpendicular height is used.

Frequently Asked Questions

A browsable list of common questions about calculating cylinder volume.