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Radius from Volume Formulas:
Cylinder: \[ r = \sqrt{\frac{V}{\pi h}} \]
Sphere: \[ r = \sqrt[3]{\frac{3V}{4\pi}} \]
Cone: \[ r = \sqrt{\frac{3V}{\pi h}} \]
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The radius from volume calculation determines the radius of a three-dimensional shape (cylinder, sphere, or cone) given its volume and, when applicable, its height. This is useful in engineering, manufacturing, and various scientific applications.
The calculator uses different formulas depending on the shape:
Cylinder: \[ r = \sqrt{\frac{V}{\pi h}} \]
Sphere: \[ r = \sqrt[3]{\frac{3V}{4\pi}} \]
Cone: \[ r = \sqrt{\frac{3V}{\pi h}} \]
Where:
Details: Calculating radius from volume is essential in design and manufacturing processes where you know the desired volume but need to determine the appropriate dimensions to achieve it.
Tips:
Q1: Why do I need to enter height for some shapes?
A: Cylinders and cones require height to determine radius from volume because multiple combinations of radius and height can produce the same volume.
Q2: What units should I use?
A: Use consistent units for all measurements. The calculator will return radius in the same length units as your input.
Q3: Can I calculate radius for other shapes?
A: This calculator handles cylinder, sphere, and cone. Other shapes may require different formulas.
Q4: How precise are the results?
A: Results are rounded to 4 decimal places. For most practical applications, this provides sufficient precision.
Q5: What if I get an error message?
A: Ensure all required fields are filled with positive numbers. For cylinder and cone, height must be greater than zero.