To find the volume of a cylindrical jar (like a jar of peanut butter), we can use the formula for the volume of a cylinder:
\[ V = \pi r^2 h \]
Where:
- \( V \) is the volume,
- \( r \) is the radius of the base,
- \( h \) is the height of the cylinder.
Given:
- The height \( h \) is 16 centimeters.
- The width (diameter) is 10 centimeters, so the radius \( r \) is half of the diameter:
\[ r = \frac{10 \text{ centimeters}}{2} = 5 \text{ centimeters} \]
Now, substituting the values into the volume formula:
\[ V = 3.14 \times (5 \text{ cm})^2 \times 16 \text{ cm} \]
Calculating \( (5 \text{ cm})^2 \):
\[ (5 \text{ cm})^2 = 25 \text{ cm}^2 \]
Next, substitute that back:
\[ V = 3.14 \times 25 \text{ cm}^2 \times 16 \text{ cm} \]
Calculating \( 25 \text{ cm}^2 \times 16 \text{ cm} \):
\[ 25 \text{ cm}^2 \times 16 \text{ cm} = 400 \text{ cm}^3 \]
Now, substituting back into the volume formula:
\[ V = 3.14 \times 400 \text{ cm}^3 \]
Now perform the multiplication:
\[ V = 1256 \text{ cm}^3 \]
Thus, the volume of the peanut butter jar is 1,256 cubic centimeters.
The correct answer is:
1,256 cubic centimeters.