Learning library

Cylinder math, explained from the measurement up

Ten independently written guides with derivations, checked examples, unit reasoning and honest limitations—not filler around a calculator.

PracticeComparisonsTanksPipesSurface areaUnitsAlgebraMeasurementFormulasFundamentals

Practice

Ten Cylinder Practice Problems With Checked Solutions

Practice direct, inverse, unit-conversion, hollow-cylinder and partial-tank calculations with concise checked answers.

10 min read • Read guide →Comparisons

Cylinder, Cone and Sphere: Ratios You Can See

Compare equal-base cylinders and cones, then a sphere with its enclosing cylinder using exact volume ratios.

7 min read • Read guide →Tanks

Why Horizontal Tank Fill Is Nonlinear

Understand the circular-segment formula, endpoint checks and practical limitations for partly filled horizontal cylinders.

9 min read • Read guide →Pipes

Hollow Cylinders, Pipe Walls and Material Volume

Calculate annular material volume, distinguish pipe capacity from wall volume and connect geometry to density.

8 min read • Read guide →Surface area

Surface Area and Volume Are Related—but Not Interchangeable

Distinguish total and lateral cylinder area, derive a missing dimension and see why surface area alone cannot determine volume.

8 min read • Read guide →Units

Cylinder Volume Unit Conversions That Stay Dimensionally Correct

Convert cubic units, litres, gallons and fluid ounces after calculating cylinder volume without losing physical meaning.

8 min read • Read guide →Algebra

Inverse Cylinder Problems: Finding Radius or Height

Rearrange cylinder volume safely, understand when data are insufficient and verify inverse answers by substitution.

8 min read • Read guide →Measurement

Measuring Cylinder Volume by Circumference

A field guide to deriving cylinder volume from circumference when the centre or diameter is inaccessible.

7 min read • Read guide →Formulas

From Diameter to Cylinder Volume Without Rounding Early

Use V = πd²h/4, measure diameter correctly and avoid the most common radius-versus-diameter mistake.

6 min read • Read guide →Fundamentals

Cylinder Volume: A Practical Foundation

Understand the cylinder volume formula, units, measurement choices and quick checks that prevent common errors.

7 min read • Read guide →

How these guides are reviewed

Each worked result is checked against the same pure calculation functions used by the interactive tools. Definitions and conversion constants are shown where they matter, and pages distinguish ideal geometry from real manufacturing or tank-calibration limits.

Methodology and limitations