To calculate the volume of a cylinder, we use the formula:
\[ V = \pi r^2 h \]
where:
- \( V \) is the volume,
- \( r \) is the radius of the cylinder,
- \( h \) is the height of the cylinder.
Given the diameter of the glass is 8 mm, the radius \( r \) can be calculated as follows:
\[ r = \frac{\text{diameter}}{2} = \frac{8 \text{ mm}}{2} = 4 \text{ mm} \]
The height of the cylinder \( h \) is given as 13 mm. Now we can plug in the values into the volume formula:
\[ V = \pi (4 \text{ mm})^2 (13 \text{ mm}) \]
Calculating the area of the base:
\[ (4 \text{ mm})^2 = 16 \text{ mm}^2 \]
Now substitute this back into the volume formula:
\[ V = \pi (16 \text{ mm}^2)(13 \text{ mm}) = \pi (208 \text{ mm}^3) \]
Now, using the approximate value of \( \pi \approx 3.14159 \):
\[ V \approx 3.14159 \times 208 \approx 652.12 \text{ mm}^3 \]
Rounding to the nearest hundredth, the volume of the cylinder is:
\[ \boxed{652.12} \text{ cubic millimeters} \]
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