To find the volume of a sphere (in this case, the marble), you can use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
where \(V\) is the volume and \(r\) is the radius of the sphere.
Given that the diameter of the marble is 13 milliliters, you can find the radius by dividing the diameter by 2:
\[ r = \frac{13}{2} = 6.5 \text{ milliliters} \]
Now, 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 substitute that value into the volume formula:
\[ V = \frac{4}{3} \pi (274.625) \]
Calculating:
\[ V \approx \frac{4}{3} \times 3.14159 \times 274.625 \approx \frac{4 \times 3.14159 \times 274.625}{3} \]
Calculating the volume:
\[ V \approx \frac{4 \times 3.14159 \times 274.625}{3} \approx \frac{3449.520}{3} \approx 1150.507 \text{ cubic milliliters} \]
So, the volume of the marble is approximately 1150.51 cubic milliliters.