Volume of Cylinder Calculator Formula

Understand the math behind the volume of cylinder calculator. Each variable explained with a worked example.

Use the Volume of Cylinder Calculator

Formulas Used

Volume

volume = pi * r^2 * h

Lateral Area

lateral_area = 2 * pi * r * h

Total Surface Area

total_surface_area = 2 * pi * r * h + 2 * pi * r^2

Base Area

base_area = pi * r^2

Variables

VariableDescriptionDefault
rRadius4
hHeight10

How It Works

How to Calculate the Volume of a Cylinder

Formula

V = π × r² × h

Where:

  • V = Volume
  • π ≈ 3.14159
  • r = radius of the base
  • h = height

    • Surface Area

  • Lateral area = 2πrh (the curved side)
  • Total area = 2πrh + 2πr² (sides + top + bottom)

    • Worked Example

    Find the volume of a cylinder with radius 4 and height 10.

    r = 4h = 10
    1. 01V = π × 4² × 10
    2. 02= π × 16 × 10
    3. 03= π × 160
    4. 04≈ 502.6548

    Frequently Asked Questions

    How do you find the volume of a cylinder?

    Multiply the area of the circular base (πr²) by the height: V = πr²h.

    What is the lateral surface area of a cylinder?

    The lateral (side) surface area is the area of the curved surface: 2πrh. Imagine unrolling the side into a rectangle with width 2πr and height h.

    Ready to run the numbers?

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