# Finding the area of a surface of revolution

Q: The curve y = sqrt(9-x^2), -1<=x<=1 is an arc of the circle x^2 + y^2 = 9. Find the area of the surface obtained by rotating this arc about the x-axis.

Note: The surface is a portion of a sphere with radius 2.

See Word attachment for cleaner version with equations using Math script.

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#### Solution Preview

A: The surface area of the surface obtained by rotating a curve about the x-axis is given by

S= int[a,b]{2(pi)y[sqrt(1+(y')^2)dx}. See Word ...

#### Solution Summary

A step-by-step solution is provided, which illustrates how to find the area of a surface of revolution, obtained from an arc being rotated about the x-axis. Finding a derivative and then integration are 2 key concepts used in the solution.

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