How this calculation works
Find the curved area traced by revolving z=a r² from the axis to a given outer radius.
THE FORMULA
A=π[(1+4a²R²)^(3/2)−1]/(6a²)A worked example
With coefficient 0.5 and radius 1, the area is about 3.83 square units.
Good to know
The circular cap is excluded. A zero coefficient gives a flat disk.
Reference: OpenStax Calculus Volume 3 (opens in a new tab) ↗
Read the result
Find the curved area traced by revolving z=a r² from the axis to a given outer radius.
The primary result is labeled “Curved surface area”. Keep the input definitions in view when comparing this result with another method.
Try a related calculation
The circular cap is excluded. A zero coefficient gives a flat disk.
For a related exercise, try the quadratic equation solver.
A few questions, answered
How can I check the default inputs by hand?
With coefficient 0.5 and radius 1, the area is about 3.83 square units.
Which rule does this calculator apply?
A=π[(1+4a²R²)^(3/2)−1]/(6a²)