To find the total surface area (SA) of a cylinder, we can use the formula:
\[ SA = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.
Given:
- \( r = 4 \) feet
- \( h = 15 \) feet
Now we will calculate each part of the formula.
-
Calculate the area of the two circular bases: \[ 2\pi r^2 = 2 \times 3.14 \times (4^2) \] \[ = 2 \times 3.14 \times 16 \] \[ = 2 \times 3.14 \times 16 = 100.48 \text{ feet}^2 \]
-
Calculate the lateral surface area: \[ 2\pi rh = 2 \times 3.14 \times 4 \times 15 \] \[ = 2 \times 3.14 \times 60 \] \[ = 2 \times 188.4 = 376.8 \text{ feet}^2 \]
-
Now, add both areas together to get the total surface area: \[ SA = 100.48 + 376.8 = 477.28 \text{ feet}^2 \]
Rounding to the nearest tenth, we have: \[ SA \approx 477.3 \text{ feet}^2 \]
Thus, the correct answer is:
- 477.3 feet².