The lateral area \( A \) of a cylinder can be calculated using the formula:
\[ A = 2 \pi r h \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.
Given:
- Radius \( r = 4 \) inches,
- Height \( h = 7 \) inches.
Now, substituting the values into the formula:
\[ A = 2 \pi (4)(7) \]
Calculating that:
\[ A = 2 \pi (28) = 56 \pi \]
To find the numerical value, we can use \( \pi \approx 3.14 \):
\[ 56 \pi \approx 56 \times 3.14 = 175.84 \]
Rounding to the nearest hundredth, we get:
\[ A \approx 175.84 \text{ square inches} \]
However, it looks like we may have misstated the available options in the summary.
Thus, the closest option to 175.84 square inches would be:
- 175.93 square inches
(It's important to note the slight discrepancy due to rounding \( \pi \)).