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Math • Cylinder Volume Calculator

Cylinder Volume Calculator

Calculate the volume, surface area, and lateral area of a cylinder from radius and height.

Volume (V = πr²h)
502.655
Total Surface Area
351.858
Lateral Area
251.327
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Calculation Guide & Reference

Cylinder Volume & Surface Area Mathematics

Cylinder volume calculator computes volume, total surface area, and lateral surface area from radius and height, using V = πr²h.

Standardized Mathematical Formula
V = πr²h

The volume of a cylinder is the area of its circular base (πr²) multiplied by its height — essentially stacking that circular area up through the height.

Variables:
r:Radius of the circular base
h:Height of the cylinder
How It Works (Step-by-Step)
  • 1Enter the radius and height of the cylinder.
  • 2View the volume, total surface area, and lateral (side-only) surface area.
Real-World Numerical Example
A Cylinder with Radius 4 and Height 10

A cylindrical tank has a radius of 4 units and a height of 10 units.

•Base area: π × 4² = 16π.
•Volume: 16π × 10 = 160π ≈ 502.65 cubic units.
Result: The cylinder's volume is approximately 502.65 cubic units.
Calculation Best Practices & Tips
Examine the discriminant (b² - 4ac) before solving quadratics to instantly know if roots are real, distinct, repeated, or complex.
In statistical analysis, always check both the mean and median to identify if data distribution is skewed by outliers.
When calculating percentage changes, ensure you divide by the original starting baseline value: ((New - Old) / Old) * 100.

Frequently Asked Questions (FAQ)

V = πr²h, where r is the radius of the circular base and h is the height — multiply the base's circular area by the height.

Total surface area is 2πr(r + h) — this accounts for the two circular ends (2πr²) plus the curved side (2πrh, the "lateral" surface area).

Any consistent length unit works (inches, cm, meters) — the result will be in that unit cubed for volume, or squared for surface area.

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