To find the volume of the jar of peanut butter, we can model it as a cylinder. 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,
- \( h \) is the height of the cylinder,
- \( \pi \) is approximately 3.14.
Given:
- The height \( h = 16 \) cm,
- The width (diameter) of the jar is 10 cm, so the radius \( r \) is half of that:
\[ r = \frac{10}{2} = 5 \text{ cm} \]
Now we can substitute the values into the volume formula:
\[ V = 3.14 \times (5)^2 \times 16 \]
Calculating \( (5)^2 \):
\[ (5)^2 = 25 \]
Now substitute back into the formula:
\[ V = 3.14 \times 25 \times 16 \]
Calculating \( 25 \times 16 \):
\[ 25 \times 16 = 400 \]
Finally, multiply:
\[ V = 3.14 \times 400 = 1,256 \]
Thus, the volume of the peanut butter jar is:
\[ \boxed{1,256} \text{ cubic centimeters} \]
Therefore, the correct answer is option 4. 1,256 cubic centimeters.