1. What is Volume of Cylinder given Total Surface Area and Radius?

The volume of a cylinder given its total surface area and radius is calculated by first determining the height from the surface area formula, then using that height to find the volume. This approach is useful when the height is unknown but the total surface area and radius are given.

2. How Does the Calculator Work?

The calculator uses the following formulas:

Where:

• \( TSA \) — Total Surface Area
• \( r \) — Radius of the cylinder
• \( h \) — Height of the cylinder
• \( V \) — Volume of the cylinder

Explanation: First, the height is calculated by rearranging the surface area formula, then the volume is calculated using the standard volume formula.

3. Importance of Volume Calculation

Details: Calculating the volume of a cylinder is essential in various fields including engineering, architecture, manufacturing, and physics. It helps in determining capacity, material requirements, and structural properties.

4. Using the Calculator

Tips: Enter the total surface area and radius in consistent units. Both values must be positive numbers. The calculator will compute the volume in cubic units.

5. Frequently Asked Questions (FAQ)

Q1: What if the calculated height is negative?
A: A negative height indicates that the given total surface area is too small for the given radius, making the cylinder impossible.

Q2: Can this calculator be used for any units?
A: Yes, as long as the units for surface area and radius are consistent, the volume will be in the corresponding cubic units.

Q3: What is the precision of the calculator?
A: The calculator provides results with up to 4 decimal places for accuracy.

Q4: Are there limitations to this calculation?
A: This calculation assumes a perfect right circular cylinder. It may not be accurate for irregular or oblique cylinders.

Q5: How is π value handled in calculations?
A: The calculator uses the PHP constant M_PI which provides a precise value of π (approximately 3.1415926535898).