Basic Shape Surface Area to Volume Ratio Calculator

Basic Shapes:

Length \( L \):

Radius \( R \):

Height \( H \):

Radius \( R \):

Height \( H \):

Radius \( R \):

Height \( H \):

Surface Area (cm²): Surface Area (in²): Surface Area (ft²): Surface Area (m²):

Volume (cm³): Volume (in³): Volume (ft³): Volume (m³):

Surface Area to Volume Ratio(l/cm): Surface Area to Volume Ratio(l/m): Surface Area to Volume Ratio(l/in):

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	\( 6L^2 \)	\( L^3 \)	\( 6/L \)
Cylinder	\( 2\pi R (R + H) \)	\( \pi R^2 H \)	\( 2 (R + H) / (R H) \)
Sphere	\( 4\pi R^2 \)	\( 4\pi R^3 / 3 \)	\( 3 / R \)
Cone	\( \pi R L + \pi R^2 \) (where \( L = \sqrt{R^2 + H^2} \))	\( \pi R^2 H / 3 \)	\( 3 (R + L) / (R H) \)
Hemisphere	\( 3\pi R^2 \)	\( 2\pi R^3 / 3 \)	\( 4.5 / R \)
Capsule	\( 2\pi R (2R + H) \)	\( \pi R^2 (4R/3 + H) \)	\( (2R + H) / (4R + 3H) \)

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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