To find the surface area of a right circular cylinder, we use the formula:
\[ SA = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height (or length) of the cylinder,
- \( \pi \) is approximately 3.14.
Given:
- Diameter = 0.50 inches, so the radius \( r \) is half of that: \[ r = \frac{0.50}{2} = 0.25 \text{ inches} \]
- Length \( h = 36 \) inches.
Now, we substitute these values into the formula:
-
Calculate the area of the two circular bases: \[ 2\pi r^2 = 2 \times 3.14 \times (0.25)^2 = 2 \times 3.14 \times 0.0625 = 2 \times 3.14 \times 0.0625 = 0.3925 \text{ inches}^2 \]
-
Calculate the lateral surface area: \[ 2\pi rh = 2 \times 3.14 \times 0.25 \times 36 = 2 \times 3.14 \times 9 = 56.52 \text{ inches}^2 \]
-
Combine both areas to find the total surface area: \[ SA = 0.3925 + 56.52 = 56.9125 \text{ inches}^2 \]
Since we are looking for a rounded answer, we can round this value: \[ SA \approx 56.91 \text{ inches}^2 \]
Among the provided options, the closest one is:
56.91 inches².