Total Surface Area Of Half Cylinder Given Space Diagonal And Radius Calculator

Formula Used:

\[ TSA = \pi r (\sqrt{d_{Space}^2 - r^2} + r) + 2r \sqrt{d_{Space}^2 - r^2} \]

Total Surface Area of Half Cylinder:

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1. What is Total Surface Area of Half Cylinder?

The Total Surface Area of a Half Cylinder is defined as the measure of the total amount of 2D space enclosed by all the faces of the Half Cylinder. It includes the curved surface area and the two flat surfaces (the rectangular face and the two semicircular ends).

2. How Does the Calculator Work?

The calculator uses the formula:

\[ TSA = \pi r (\sqrt{d_{Space}^2 - r^2} + r) + 2r \sqrt{d_{Space}^2 - r^2} \]

Where:

\( TSA \) — Total Surface Area of Half Cylinder (m²)
\( r \) — Radius of Half Cylinder (m)
\( d_{Space} \) — Space Diagonal of Half Cylinder (m)
\( \pi \) — Archimedes' constant (approximately 3.14159)

3. Formula Explanation

Details: The formula calculates the total surface area by considering both the curved surface area and the flat surfaces of the half cylinder, using the space diagonal and radius as inputs.

4. Using the Calculator

Tips: Enter the radius and space diagonal values in meters. Both values must be positive numbers, and the space diagonal must be greater than the radius for valid results.

5. Frequently Asked Questions (FAQ)

Q1: What is a Space Diagonal in a Half Cylinder?
A: Space Diagonal of a Half Cylinder is a line connecting two vertices that are not on the same face of the Half Cylinder.

Q2: Why must Space Diagonal be greater than Radius?
A: According to the Pythagorean theorem, the space diagonal must be greater than the radius to form a valid right triangle with the height of the cylinder.

Q3: What are the units of measurement?
A: The calculator uses meters for both input values and returns square meters for the surface area result.

Q4: Can this calculator handle decimal values?
A: Yes, the calculator accepts decimal values with up to 4 decimal places precision.

Q5: What if I get an error message?
A: Ensure both input values are positive numbers and that the space diagonal is greater than the radius.