A capsule is a three-dimensional geometric shape consisting of a cylinder with hemispherical ends. This calculator determines the volume of a capsule using the radius and the length of the cylindrical portion.
Formula
The volume of a capsule is calculated as:
[V_c = \pi r^2 \left(\frac{4}{3}r + h\right)]
Where:
- r is the radius of the capsule (both cylinder and hemispheres)
- h is the length of the cylindrical side (excluding the hemispherical ends)
- π (pi) ≈ 3.14159
This formula combines:
- Cylinder volume: πr²h
- Sphere volume: (4/3)πr³
Calculation Example
For a capsule with radius 25 inches and cylindrical side length 40 inches:
Step 1: Identify the values
- r = 25 inches
- h = 40 inches
Step 2: Calculate the volume
[V_c = \pi \times 25^2 \times \left(\frac{4}{3} \times 25 + 40\right)]
[V_c = \pi \times 625 \times (33.33 + 40)]
[V_c = \pi \times 625 \times 73.33]
[V_c \approx 143,989.66 \text{ cubic inches}]
Volume Components
A capsule's volume consists of:
| Component | Formula | Contribution |
|---|---|---|
| Cylindrical portion | πr²h | Variable based on length |
| Two hemispheres (one sphere) | (4/3)πr³ | Fixed for given radius |
| Total capsule | πr²((4/3)r + h) | Combined volume |
Applications
- Pharmaceuticals: Designing pill and capsule medications
- Engineering: Fuel tanks, pressure vessels, and storage containers
- Architecture: Rounded structures and decorative elements
- Manufacturing: Product packaging and container design
- Marine Engineering: Submarine hull sections and buoyancy calculations
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