Surface Area Of Hollow Sphere Given Thickness And Outer Radius Calculator

Surface Area of Hollow Sphere Formula:

\[ SA = 4\pi(r_{Outer}^2 + (r_{Outer} - t)^2) \]

Surface Area of Hollow Sphere:

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1. What is Surface Area of Hollow Sphere?

The surface area of a hollow sphere is the total quantity of two dimensional space enclosed by the spherical surface. It represents the sum of the outer surface area and the inner surface area of the hollow sphere.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ SA = 4\pi(r_{Outer}^2 + (r_{Outer} - t)^2) \]

Where:

\( SA \) — Surface Area of Hollow Sphere (m²)
\( r_{Outer} \) — Outer Radius of Hollow Sphere (m)
\( t \) — Thickness of Hollow Sphere (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

Explanation: The formula calculates the total surface area by summing the outer surface area and the inner surface area of the hollow sphere.

3. Importance of Surface Area Calculation

Details: Calculating the surface area of hollow spheres is important in various engineering applications, material science, and physics, particularly when dealing with heat transfer, pressure vessels, and structural design.

4. Using the Calculator

Tips: Enter the outer radius and thickness in meters. Both values must be positive, and the thickness must be less than the outer radius for a valid hollow sphere.

5. Frequently Asked Questions (FAQ)

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

Q2: How is this different from a solid sphere's surface area?
A: A solid sphere has only one surface area (4πr²), while a hollow sphere has both outer and inner surface areas that need to be calculated.

Q3: What are the units for surface area?
A: Surface area is measured in square units (m², cm², etc.), matching the square of the units used for radius and thickness.

Q4: Can this formula be used for any thickness value?
A: The thickness must be less than the outer radius to form a valid hollow sphere. If thickness equals outer radius, the inner radius becomes zero.

Q5: What are practical applications of hollow spheres?
A: Hollow spheres are used in pressure vessels, ball bearings, architectural structures, and various engineering components where weight reduction is important.