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Basic Shape Surface Area to Volume Ratio Calculator





1. What is a Surface Area to Volume Ratio Calculator?

Definition: This calculator computes the surface area, volume, and surface area to volume ratio for various basic shapes.

Purpose: Useful for understanding geometric properties in mathematics, biology, and engineering.

2. Formulas

Shape Surface Area Volume Surface Area to Volume Ratio
Cube 6L2 L3 6/L
Cylinder 2πR(R+H) πR2H 2(R+H)/(RH)
Sphere 4πR2 4πR3/3 3/R
Cone πRL+πR2 (where L=R2+H2) πR2H/3 3(R+L)/(RH)
Hemisphere 3πR2 2πR3/3 4.5/R
Capsule 2πR(2R+H) πR2(4R/3+H) (2R+H)/(4R+3H)

Unit Conversions:

  • Input (Length): mm (×0.1), cm (×1), m (×100), in (×2.54), ft (×30.48)
  • Surface Area: cm² (direct), in² (×0.155), ft² (×0.00107639), m² (×0.0001)
  • Volume: cm³ (direct), in³ (×0.0610237), ft³ (×0.0000353147), m³ (×0.000001)
Explanation: Inputs are converted to cm, surface area is calculated in cm², volume in cm³, and ratios are unitless, with conversions to other units applied.

3. Importance of Surface Area to Volume Ratio

Details: The surface area to volume ratio is crucial in biology (e.g., cell efficiency), engineering (e.g., heat dissipation), and material science.

4. Using the Calculator

Tips: Select a shape and enter the required dimensions (length, radius, height) in mm, cm, m, in, or ft (all >0). Results show surface area (cm², in², ft², m²), volume (cm³, in³, ft³, m³), and the ratio.

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