If we have a curve lying entirely on or above the x-axis, which is the
graph of a function *f*(*x*), and x is restricted to being between *a*
and *b*, then we may rotate it about the x-axis, generating a three
dimensional object; a *solid of revolution*.

For example, if the curve is simply *f*(*x*) = *ax*/*h* (a straight line)
and x is between 0 and h, we obtain a *cone* of height *h* and radius *a*.

If and x is between, say, 0 and 1, we obtain a bowl
shaped object called a *paraboloid*. (Note the equation is equivalent to , a parabola).

If and x is between -*a* and *a*,
we obtain a *sphere* of radius *a* (since the equation is equivalent to , a circle of radius
*a*).

The textbook (p. 388) develops the formula that the **volume** of
the solid obtained by rotating about the x-axis is given by

The volume is obtained by adding up volumes of cylindrical disks,
while its **surface area** (p. 400) is given by

Note that both of these formulas are for rotating the graph of *f*(*x*)
about the **x-axis**.

Tue Dec 3 12:06:23 EST 1996