To calculate the surface area of a right circular cylinder, we use the formula:
\[ \text{Surface Area} = 2\pi r^2 + 2\pi rh \]
Where:
- \( r \) is the radius of the cylinder
- \( h \) is the height of the cylinder
From the problem, we know:
- The top and bottom of the cylinder are circles with a diameter of 5 inches. Therefore, the radius \( r \) is half of the diameter:
\[ r = \frac{5}{2} = 2.5 \text{ inches} \]
- The height \( h \) of the cylinder is given as 4 inches.
Now substituting the values into the formula, we calculate the surface area.
- First, calculate \( 2\pi r^2 \) (the area of the top and bottom):
\[ 2\pi r^2 = 2 \times 3.14 \times (2.5)^2 \]
Calculating \( (2.5)^2 \):
\[ (2.5)^2 = 6.25 \]
Now, substituting that back in:
\[ 2\pi r^2 = 2 \times 3.14 \times 6.25 = 39.25 \text{ inches}^2 \]
- Next, calculate \( 2\pi rh \) (the area of the side of the cylinder):
\[ 2\pi rh = 2 \times 3.14 \times 2.5 \times 4 \]
Calculating \( 2.5 \times 4 \):
\[ 2.5 \times 4 = 10 \]
Now substituting that back in:
\[ 2\pi rh = 2 \times 3.14 \times 10 = 62.8 \text{ inches}^2 \]
- Finally, sum both areas to find the total surface area:
\[ \text{Surface Area} = 39.25 + 62.8 = 102.05 \text{ inches}^2 \]
However, it appears that you have listed some responses that do not include 102.05 inches². Let's check the values derived or provided in the responses:
Given Options:
- 157 inches²
- 282.6 inches²
- 141.3 inches²
- 197 inches²
Hence, it seems in the calculations or interpretations, a critical element may have been misread—for example, height or shape details. Please double-check. Based on this analysis and standard cylinder geometry:
The correct calculated answer appears not present among the options provided. The correct surface area derived above is 102.05 inches².