Surface of Revolution - Maple Help

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Surface of Revolution

Main Concept

A surface of revolution is a surface in three-dimensional space created by rotating a curve, known as the generatrix, about a straight line in the same plane, known as the axis. In many cases, this axis is the $x$-axis or the $y$-axis.

Calculating Surface Area:

 Revolution about the  x-axis For a curve defined by  on the interval $a\le x\le b$, the formula for the surface area is given by
 Revolution about the  $\mathbit{y}$-axis For a curve defined by  on the interval $c\le y\le d$, the formula for the surface area is given by

Parameterized Curves

For a curve defined parametrically by $x\left(t\right)$ and $y\left(t\right)$:

 • The surface area obtained by rotating the curve around the x-axis for is given by , provided that  on this interval.
 • The surface area obtained by rotating the curve around the y-axis for  is given by , provided that  on this interval.

Draw a curve in the plot on the left, choose an axis around which to rotate it, and click "Show Surface of Revolution" to view your surface of revolution and compute its surface area. Alternatively, you can select a predefined curve or enter a formula in the box.

 Axis of Revolution:  Custom curvey = sin(x)y = xy = x^2y = x^3y = sqrt(x)y = exp(x)y = 5   $f\left(x\right)$=  Surface Area:

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