To find the volume of a sphere, you can use the formula:
\[ V = \frac{4}{3} \pi r^3 \]
where \( V \) is the volume and \( r \) is the radius of the sphere.
- Calculate the radius: The radius is half of the diameter. Given that the diameter is 13 millimeters, the radius is:
\[ r = \frac{13}{2} = 6.5 \text{ mm} \]
- Calculate the volume using the formula:
\[ V = \frac{4}{3} \pi (6.5)^3 \]
- Calculate \( (6.5)^3 \):
\[ (6.5)^3 = 6.5 \times 6.5 \times 6.5 = 274.625 \]
- Substituting into the volume formula:
\[ V = \frac{4}{3} \pi (274.625) \]
- Calculate the volume:
Using \( \pi \approx 3.14159 \):
\[ V \approx \frac{4}{3} \times 3.14159 \times 274.625 \approx \frac{4 \times 3.14159 \times 274.625}{3} \]
Calculating this step by step:
\[ 4 \times 3.14159 \approx 12.56636 \]
Then multiply by \( 274.625 \):
\[ 12.56636 \times 274.625 \approx 3457.791 \]
Now divide by 3:
\[ \frac{3457.791}{3} \approx 1152.597 \]
Thus, the volume of the marble is approximately:
\[ V \approx 1152.6 \text{ mm}^3 \]
The closest measurement to the calculated volume (1152.6 mm³) from the provided options is:
1,150 mm³.