Radius of Cylinder given Total Surface Area and Base Area Calculator

Formula Used:

\[ r = \frac{TSA - 2 \times BA}{2 \times \pi \times \sqrt{BA \div \pi}} \]

Radius (r):

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1. What is the Radius of Cylinder Formula?

The formula calculates the radius of a cylinder when given its total surface area and base area. It's derived from the standard cylinder surface area formula and provides an efficient way to determine the radius without needing height measurements.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ r = \frac{TSA - 2 \times BA}{2 \times \pi \times \sqrt{BA \div \pi}} \]

Where:

\( r \) — Radius of the cylinder
\( TSA \) — Total surface area of the cylinder
\( BA \) — Base area of the cylinder
\( \pi \) — Mathematical constant (approximately 3.14159)

Explanation: The formula rearranges the standard cylinder surface area equation to solve for radius when total surface area and base area are known.

3. Importance of Radius Calculation

Details: Calculating the radius is essential for various engineering and design applications involving cylindrical structures, containers, pipes, and mechanical components where surface area measurements are available but radius needs to be determined.

4. Using the Calculator

Tips: Enter total surface area and base area in square meters. Both values must be positive numbers. The calculator will compute the radius automatically.

5. Frequently Asked Questions (FAQ)

Q1: Why is this formula useful?
A: This formula allows calculation of cylinder radius when you know the total surface area and base area but don't have height measurements.

Q2: What are typical units for these measurements?
A: Surface area and base area are typically measured in square meters (m²) or square centimeters (cm²), while radius is in meters (m) or centimeters (cm).

Q3: Can this formula be used for any cylinder?
A: Yes, this formula works for right circular cylinders where the bases are perfect circles.

Q4: What if I get a negative result?
A: A negative result indicates invalid input values where the total surface area is less than twice the base area, which is mathematically impossible for a cylinder.

Q5: How accurate is this calculation?
A: The calculation is mathematically precise based on the input values. Accuracy depends on the precision of your surface area and base area measurements.