To calculate the volume of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
where \( V \) is the volume, \( r \) is the radius, and \( h \) is the height. Given that the radius \( r = 4 \) inches, the height \( h = 10 \) inches, and using \( \pi \approx 3.14 \), we can substitute these values into the formula:
\[ V = 3.14 \times (4)^2 \times 10 \]
Calculating \( (4)^2 \):
\[ (4)^2 = 16 \]
Now substitute back into the volume formula:
\[ V = 3.14 \times 16 \times 10 \]
Calculating \( 16 \times 10 \):
\[ 16 \times 10 = 160 \]
Now multiply by \( 3.14 \):
\[ V = 3.14 \times 160 = 502.4 \]
Thus, the volume of the cylinder is:
\[ \boxed{502.4 \text{ in}^3} \]
So the correct answer is 502.4 in³.