Volume of a Solid of Revolution Around the x-Axis

This example visualizes the volume of a solid formed by rotating a function curve around the x-axis, linking the 3D geometry with the computed integral value. It highlights core ideas of the solid-of-revolution method (disk/washers/infinitesimal “slices”), the use of definite/indefinite integrals, and typical function relationships that may involve trigonometric expressions, similarity-style transformations, and arithmetic-mean logic when defining bounds or combining parts. Construction is done in GeoGebra by using Textfield to set and display parameters and labels, Integral to compute the volume, and Surface to generate the rotated 3D solid. FractionText is used to show key fractional expressions and results clearly. The build uses objects such as f, d, e, multiple InputBox controls (InputBox1/2/3), parameters like a, b, a_1, b_1, c, g, h, i, and outputs/annotations like vol, voldpi, and text1–text3. Suitable for high school–early college calculus, teaching integral applications and 3D geometric visualization.