To find the volume of a sphere, we use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius of the sphere.
Given that the diameter of the sphere is 13 millimeters, we can find the radius by dividing the diameter by 2:
\[ r = \frac{13}{2} = 6.5 \text{ mm} \]
Now, we can substitute the radius into the volume formula:
\[ V = \frac{4}{3} \pi (6.5)^3 \]
Calculating \( (6.5)^3 \):
\[ (6.5)^3 = 6.5 \times 6.5 \times 6.5 = 274.625 \]
Now substituting back into the volume formula:
\[ V = \frac{4}{3} \pi (274.625) \]
Now, calculating \( \frac{4}{3} \times 274.625 \):
\[ \frac{4}{3} \times 274.625 \approx 366.167 \]
Now, calculating the volume with \( \pi \):
\[ V \approx 366.167 \times 3.14159 \approx 1,150.56 \text{ mm}^3 \]
Thus, the closest measurement to the volume of the marble in cubic millimeters is:
1,150 mm³