Three-dimensional geometric solids enclose volume based on fundamental radius, height, and length dimensions. Whether calculating the capacity of an industrial chemical storage tank, the internal volume of a shipping carton, or the displacement of a spherical pressure vessel, this calculator computes total volume alongside metric liter and imperial gallon liquid equivalents.

### Geometric Volume Formulas

Calculations apply classical Euclidean volumetric formulas for standard 3D solids: 1. **Cylinder (Round Tank, Pipe, Rod):** $$V = \pi \times r^2 \times h$$ 2. **Sphere (Ball, Spherical Tank, Bubble):** $$V = \frac{4}{3} \times \pi \times r^3$$ 3. **Cone (Funnel, Hopper, Pile):** $$V = \frac{1}{3} \times \pi \times r^2 \times h$$ 4. **Rectangular Box / Prism (Shipping Carton, Room, Container):** $$V = l \times w \times h$$

### Standard Liquid Capacity Conversions

- **Cubic Centimeters to Liters ($1\text{ L} = 1,000\text{ cm}^3$):** $$\text{Volume (Liters)} = \frac{V_{\text{cm}^3}}{1000}$$ - **Cubic Inches to US Liquid Gallons ($1\text{ gal} = 231\text{ in}^3$):** $$\text{Volume (Gallons)} = \frac{V_{\text{in}^3}}{231}$$

### Worked Calculation Examples

- **Example 1: Cylindrical Tank ($r = 4.0\text{ in}, h = 10.0\text{ in}$):** $$V = \pi \times 4^2 \times 10 = \pi \times 16 \times 10 \approx \mathbf{502.65\text{ cu in}}$$ $$\text{Gallon Capacity} = 502.65 / 231 \approx \mathbf{2.18\text{ US gallons}}$$ - **Example 2: Shipping Box ($l = 12\text{ in}, w = 10\text{ in}, h = 8\text{ in}$):** $$V = 12 \times 10 \times 8 = \mathbf{960.00\text{ cu in}} \approx 4.16\text{ gallons}$$

### Pure Client-Side Computation

All geometric calculations execute locally in your browser runtime via standard JavaScript floating-point arithmetic. No dimensional records or calculation parameters leave your device.