1. What is a Sphere Volume Calculator?

Definition: This calculator computes the volume and circumference of a sphere, a perfectly round three-dimensional object, based on its radius (\( r \)).

Purpose: Useful in geometry, physics, and engineering for determining the volume and circumference of spherical objects (e.g., balls, planets).

2. How Does the Calculator Work?

The calculations are based on the following formulas:

Unit Conversions:

• Input (Length): mm (×0.1), cm (×1), m (×100), in (×2.54), ft (×30.48) to cm
• Volume (from cm³): m³ (×0.000001), in³ (×0.0610237), ft³ (×0.0000353147), liters (×0.001)
• Circumference (from cm): m (×0.01), in (×0.393701), ft (×0.0328084)

Explanation: The radius is converted to cm, the volume and circumference are calculated, and then converted to other units.

3. Importance of Sphere Volume and Circumference Calculation

Details: Calculating the volume and circumference of a sphere is essential in physics (e.g., calculating planetary volumes), engineering (e.g., designing spherical containers), and everyday applications (e.g., determining the capacity of spherical objects).

4. Using the Calculator

Tips: Enter the radius \( r \) in mm, cm, m, in, or ft (must be >0). The result shows the volume in cm³, m³, in³, ft³, and liters, and the circumference in cm, m, in, and ft.

5. Example

Given: Radius \( r = 5 \, \text{cm} \).
Volume Calculation: \( V = \frac{4}{3} \times \pi \times 5^3 \approx 523.599 \, \text{cm}^3 \).
Circumference Calculation: \( \text{Circumference} = 2 \times \pi \times 5 \approx 31.416 \, \text{cm} \).
Conversions (Volume):
- \( \text{cm}^3 \approx 523.599 \),
- \( \text{m}^3 \approx 0.000524 \),
- \( \text{in}^3 \approx 31.942 \),
- \( \text{ft}^3 \approx 0.0185 \),
- \( \text{liters} \approx 0.524 \).
Conversions (Circumference):
- \( \text{cm} \approx 31.416 \),
- \( \text{m} \approx 0.314 \),
- \( \text{in} \approx 12.368 \),
- \( \text{ft} \approx 1.031 \).

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