To calculate the surface area of a right circular cylinder, we need to include the areas of the two circular bases and the rectangular side (lateral surface area).
The formula for the surface area \( S \) of a right circular cylinder is given by:
\[ S = 2\pi r^2 + 2\pi rh \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
From the problem:
- The height \( h = 5 \) inches (assuming this as the height),
- The radius \( r = 4 \) inches.
Now we can plug these values into the surface area formula.
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Calculate the area of the two circular bases: \[ 2\pi r^2 = 2 \times 3.14 \times (4)^2 = 2 \times 3.14 \times 16 = 100.48 \text{ inches}^2 \]
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Calculate the lateral surface area: \[ 2\pi rh = 2 \times 3.14 \times 4 \times 5 = 2 \times 3.14 \times 20 = 125.6 \text{ inches}^2 \]
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Add both areas to find the total surface area: \[ S = 100.48 + 125.6 = 226.08 \text{ inches}^2 \]
None of the options given (157 inches², 282.6 inches², 141.3 inches², or 197 inches²) match the calculated surface area of 226.08 inches².
Please check the dimensions given in the question. If the height is indeed 5 inches and the radius is 4 inches, the calculated answer must be correct. If there is a mistake in the dimensions or assumptions, please clarify for a more accurate result.