Surface of Revolution - Maple Programming 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 y = fx>0 on the interval axb, the formula for the surface area is given by

Sx=2πabfx1+f x2ⅆx = 2πaby1+ⅆ yⅆ x2ⅆx

 

Revolution about the  y-axis

For a curve defined by x = gy > 0 on the interval cyd, the formula for the surface area is given by

Sy=2πcdgy1+gy2ⅆy = 2πcdx1+ⅆ xⅆ y 2ⅆy

Parameterized Curves

For a curve defined parametrically by xt and yt:

• 

The surface area obtained by rotating the curve around the x-axis for t a,b is given by Sx=2πabytⅆ xⅆ t2 + ⅆ yⅆ t2 ⅆt, provided that yt > 0 on this interval.

• 

The surface area obtained by rotating the curve around the y-axis for t  c,d is given by Sy=2πcdxtⅆ xⅆ t2 + ⅆ yⅆ t2 ⅆt, provided that xt > 0 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:

   fx=

 

 

 

 

 

Surface Area:

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