Explanation:
The formula for the volume (V) of a cylinder is given by:
\[ V = \pi r^2 h \]
where \( r \) is the radius of the base and \( h \) is the height.
The diameter (\( d \)) is twice the radius (\( r \)), so \( r = \frac{d}{2} \).
Given a base diameter of 10 inches, the radius (\( r \)) is \( \frac{10}{2} = 5 \) inches. The height (\( h \)) is 19 inches.
Now, substitute these values into the formula:
\[ V = \pi \times (5)^2 \times 19 \]
Calculate this expression to find the volume, and round to the nearest tenth.
Let's calculate the volume of the cylinder:
\[ V = \pi \times (5)^2 \times 19 \]
\[ V \approx 475.647 \, \text{cubic inches} \]
Rounding to the nearest tenth, the volume is approximately \( 475.6 \) cubic inches.