Surface Area of Hollow Sphere given Volume and Outer Radius Calculator

Formula Used:

\[ SA = 4 \times \pi \times \left( r_{Outer}^2 + \left( r_{Outer}^3 - \frac{3V}{4\pi} \right)^{\frac{2}{3}} \right) \]

Surface Area of Hollow Sphere:

Unit Converter ▲

Unit Converter ▼

From:	To:

1. What is the Surface Area of Hollow Sphere?

The Surface Area of a Hollow Sphere refers to the total area covered by its outer and inner surfaces. It is a key geometric property used in various engineering and mathematical applications.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ SA = 4 \times \pi \times \left( r_{Outer}^2 + \left( r_{Outer}^3 - \frac{3V}{4\pi} \right)^{\frac{2}{3}} \right) \]

Where:

\( SA \) — Surface Area of Hollow Sphere (m²)
\( r_{Outer} \) — Outer Radius of Hollow Sphere (m)
\( V \) — Volume of Hollow Sphere (m³)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: This formula calculates the surface area based on the given outer radius and volume of the hollow sphere, considering both the outer and inner surfaces.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of a hollow sphere is important in fields like material science, physics, and engineering for determining properties like heat transfer, material requirements, and structural design.

4. Using the Calculator

Tips: Enter the outer radius in meters and the volume in cubic meters. Both values must be positive. The calculator will compute the surface area based on these inputs.

5. Frequently Asked Questions (FAQ)

Q1: What is a hollow sphere?
A: A hollow sphere is a three-dimensional object with an outer and inner spherical surface, creating a hollow interior.

Q2: How is the surface area different from volume?
A: Surface area measures the total area of the surface, while volume measures the space enclosed within the object.

Q3: Can this calculator handle different units?
A: The calculator uses meters for radius and cubic meters for volume. Convert your measurements to these units before input.

Q4: What if I get a negative value inside the calculation?
A: This indicates an error in input values. Ensure the volume is appropriate for the given outer radius.

Q5: Is the formula accurate for all hollow spheres?
A: The formula is mathematically derived for perfect hollow spheres. Real-world applications may require adjustments for imperfections.