To find the volume of a cylinder, we use the formula:
\[ V = \pi r^2 h \]
where \( r \) is the radius and \( h \) is the height of the cylinder.
Given the dimensions:
- Diameter = 13 mm, therefore the radius \( r = \frac{13}{2} = 6.5 \) mm
- Height \( h = 8 \) mm
Now, substituting the values into the formula:
\[ V = \pi (6.5)^2 (8) \]
Calculating \( (6.5)^2 \):
\[ (6.5)^2 = 42.25 \]
Now, substituting this back into the volume formula:
\[ V = \pi (42.25)(8) \]
Calculating \( 42.25 \times 8 \):
\[ 42.25 \times 8 = 338 \]
So now we have:
\[ V = \pi (338) \]
Using the approximation \( \pi \approx 3.14159 \):
\[ V \approx 3.14159 \times 338 \approx 1064.63 \text{ cubic millimeters} \]
Rounding to the nearest hundredth, the volume of the cylinder is approximately:
\[ 1064.63 \text{ mm}^3 \]
As this does not correspond to the numbers you provided (471, 235.5, 1177.5, 1177.5), please verify the dimensions or options again. If the calculations and dimensions are correct, then the appropriate answer is around 1064.63 mm³.
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