To determine what happens to the surface area of a cylinder when both its radius and height are doubled, let's first look at the formula for the surface area (SA) of a cylinder:
\[ SA = 2\pi r(h + r) \]
where:
- \( r \) is the radius,
- \( h \) is the height.
Now, if both the radius and height are doubled, the new radius \( r' \) and new height \( h' \) would be:
\[ r' = 2r \] \[ h' = 2h \]
Substituting these new values into the surface area formula gives:
\[ SA' = 2\pi r'(h' + r') = 2\pi (2r)(2h + 2r) = 2\pi (2r)(2(h + r)) \]
This simplifies to:
\[ SA' = 2\pi (2r)(2(h + r)) = 2\pi (4r(h + r)) = 4(2\pi r(h + r)) = 4SA \]
Thus, the new surface area is four times the original surface area.
Therefore, if both the radius and height are doubled, the surface area of the cylinder is quadrupled.
So, the correct response is: The surface area is quadrupled.