The lateral area (or curved surface area) of a cylinder can be calculated using the formula:
\[ L = 2 \pi r h \]
where:
- \( L \) is the lateral area,
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.
In this case, the radius \( r = 7 \) in and the height \( h = 10 \) in. Substituting these values into the formula, we get:
\[ L = 2 \times \pi \times 7 \times 10 \] \[ L = 2 \times 3.14 \times 7 \times 10 \] \[ L = 2 \times 3.14 \times 70 \] \[ L = 2 \times 219.8 \] \[ L = 439.6 , \text{in}^2 \]
The correct calculation for the lateral area of the cylinder is 439.6 in².