To find the height of the right circular cylinder, we start by using the formula for the surface area of a right circular cylinder:
\[ \text{Surface Area} = 2\pi r(h + r) \]
where:
- \( r \) is the radius of the base of the cylinder,
- \( h \) is the height of the cylinder.
In this case, we're given that the radius \( r = 3 \) feet and the surface area is \( 395.64 \) square feet.
Substituting the values into the formula gives us:
\[ 395.64 = 2 \cdot \pi \cdot 3(h + 3) \]
Using \( \pi \approx 3.14 \):
\[ 395.64 = 2 \cdot 3.14 \cdot 3(h + 3) \]
Calculating the left side:
\[ 2 \cdot 3.14 \cdot 3 = 18.84 \]
Now our equation looks like this:
\[ 395.64 = 18.84(h + 3) \]
Dividing both sides by 18.84:
\[ h + 3 = \frac{395.64}{18.84} \]
Calculating the right side:
\[ h + 3 \approx 21 \]
Subtracting 3 from both sides:
\[ h \approx 21 - 3 \] \[ h \approx 18 \]
Thus, the height \( h \) of the cylinder is approximately 18 feet.