Final Answer:
The surface area generated by rotating the given curve about the y-axis is

Step-by-step explanation:
To find the surface area generated by rotating the curve
and
about the y-axis, we use the formula for the surface area of revolution:

In this case, the integral is with respect to t since the parametric equations are given in terms of t. The limits of integration, a and b, correspond to the given interval for t, which is 0, 9. The expression inside the integral represents the differential arc length of the curve.
The parametric equations are
and
Taking the derivative
, we find
. Substituting these into the surface area formula, we integrate from 0 to 9.
The final numerical evaluation of the integral yields the surface area of approximately 99.32 units
This result represents the total surface area generated by rotating the curve about the y-axis within the specified interval.