To find the volume of the peanut butter jar, we first note that it can be approximated as a cylinder. The formula for the volume \( V \) of a cylinder is:
\[ V = \pi r^2 h \]
where:
- \( r \) is the radius of the base,
- \( h \) is the height,
- \( \pi \) is a constant approximately equal to 3.14.
Given:
- Height \( h = 16 \) cm,
- Width (diameter) = 10 cm, so the radius \( r = \frac{10}{2} = 5 \) cm.
Now, we can substitute these values into the volume formula:
\[ V = 3.14 \times (5)^2 \times 16 \]
Calculating \( r^2 \):
\[ (5)^2 = 25 \]
Now substituting that back into our volume equation:
\[ V = 3.14 \times 25 \times 16 \]
Calculating \( 25 \times 16 \):
\[ 25 \times 16 = 400 \]
Now substituting this value into the equation:
\[ V = 3.14 \times 400 \]
Calculating \( 3.14 \times 400 \):
\[ V = 1256 \]
Thus, the volume of the peanut butter jar is:
\[ \boxed{1256} \text{ cubic centimeters} \]
So, the correct response is 1,256 cubic centimeters.