Volume of a Solid of Revolution

Introduction to Volume of a Solid of Revolution

The volume of a solid of revolution is the volume of the solid generated by rotating a shape around an axis. For a solid obtained by rotating a circle around its axis, the formula to calculate the volume is V = πr^2h, where V is the volume, r is the radius of the circle, and h is the height of the solid along the axis of rotation. This formula is important in calculus and engineering to calculate the volume of objects of revolution.

Parameter usage:

• r= radius of the circle
• h= height of the solid along the axis of rotation

Output:

• V= volume of the solid

Data validation

The radius and height should be non-negative numbers.

Summary

This formula calculates the volume of a solid obtained by rotating a circle around its axis, based on the given radius and height. The output is in cubic units. It is widely used in mathematical and engineering calculations.