To find the volume \( V \) of a cylinder, you can use the formula:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.
Given:
-
The diameter of the cylinder is 16 inches, so the radius \( r \) is half of the diameter: \[ r = \frac{16}{2} = 8 \text{ inches} \]
-
The height \( h \) is 7 inches.
Now, substituting the values into the volume formula:
\[ V = 3.14 \times (8)^2 \times 7 \]
Calculating \( 8^2 \):
\[ 8^2 = 64 \]
Now substituting this into the formula:
\[ V = 3.14 \times 64 \times 7 \]
Next, calculate \( 64 \times 7 \):
\[ 64 \times 7 = 448 \]
Now multiply by \( 3.14 \):
\[ V = 3.14 \times 448 \]
Calculating this gives:
\[ V = 1406.72 \]
Rounding to the nearest hundredth, the volume of the cylinder is:
\[ \boxed{1406.72} \text{ cubic inches} \]