To calculate the height of the cylinder given its surface area, we can use the formula for the surface area \( S \) of a cylinder, which is given by:
\[ S = 2\pi r(h + r) \]
Where:
- \( S \) is the surface area,
- \( r \) is the radius,
- \( h \) is the height.
Given that the surface area \( S \) is 3,106.716 square feet, we can rearrange the formula to solve for height \( h \):
\[ 3,106.716 = 2\pi r(h + r) \]
However, to find the height \( h \), we need either the radius \( r \) or more information relating to it.
Assuming we do not have a specific radius, we need to derive an expression for \( h \) in terms of \( r \):
- Rearranging the equation for \( h \):
\[ h = \frac{3,106.716}{2\pi r} - r \]
Substituting \( \pi \approx 3.14 \):
\[ h = \frac{3,106.716}{2 \times 3.14 r} - r \]
\[ h = \frac{3,106.716}{6.28 r} - r \]
If you know the radius \( r \), you can substitute it into the equation above to find the height \( h \).
Please provide the radius \( r \) of the cylinder so that we can calculate the height accurately. If no radius is given and you need a specific height using a particular radius, please specify that radius.