The surface area of a frustum is given by,
and l is the length of the slant of the frustum.
For the frustum on the interval we have,
and we know from the previous section that,
Before writing down the formula for the surface area we are going to assume that is “small” and since is continuous we can then assume that,
So, the surface area of the frustum on the interval is approximately,
The surface area of the whole solid is then approximately,
and we can get the exact surface area by taking the limit as n goes to infinity.
If we wanted to we could also derive a similar formula for rotating on about the y-axis. This would give the following formula.
hope it helps best my answer please
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