Math • Surface Area of a Cylinder Calculator
Surface Area of a Cylinder Calculator
Calculate the total and lateral surface 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 Surface Area Mathematics
Surface area of a cylinder calculator computes total and lateral surface area from radius and height, using 2πr(r+h).
Standardized Mathematical Formula
Total SA = 2πr(r + h) = 2πr² + 2πrh
Total surface area combines the two circular end caps (2πr² total) with the curved lateral surface (2πrh) wrapping around the side.
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 total surface area and the lateral (side-only, no end caps) surface area separately.
Real-World Numerical Example
A Cylinder with Radius 4 and Height 10
A cylindrical can has a radius of 4 units and a height of 10 units.
•End caps: 2 × π × 4² = 32π.
•Lateral surface: 2π × 4 × 10 = 80π.
•Total: 32π + 80π = 112π ≈ 351.86 square units.
Result: Total surface area is approximately 351.86 square units (of which 251.33 is the lateral/side surface).
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)
Total surface area = 2πr(r + h) = 2πr² (the two circular ends) + 2πrh (the curved side).
Lateral surface area (2πrh) is just the curved side, excluding the top and bottom circles; total surface area adds the two end caps (2πr²) on top of that.
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