To calculate the volume of a right circular cylinder, we use the formula:
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius,
- \( h \) is the height,
- \( \pi \) is approximately 3.14.
Given:
- Height (\( h \)) = 15.6 inches
- Radius (\( r \)) = 5.9 inches
- \( \pi \) = 3.14
Now, substituting the values into the formula:
\[ V = 3.14 \times (5.9)^2 \times 15.6 \]
First, calculate \( (5.9)^2 \):
\[ (5.9)^2 = 34.81 \]
Next, substitute this value back into the volume formula:
\[ V = 3.14 \times 34.81 \times 15.6 \]
Now calculate \( 3.14 \times 34.81 \):
\[ 3.14 \times 34.81 \approx 109.6 \]
Finally, multiply this result by 15.6:
\[ V \approx 109.6 \times 15.6 \approx 1714.56 \]
So, rounding to the nearest tenth, the volume of the paint bucket is:
\[ \boxed{1714.6} \text{ inches}^3 \]