To find the volume of a glass marble, which is shaped like a sphere, we can use the formula for the volume of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
Where:
- \( V \) is the volume,
- \( \pi \) is approximately 3.14,
- \( r \) is the radius of the sphere.
Given the diameter of the marble is 17 millimeters, we can find the radius by dividing the diameter by 2:
\[ r = \frac{17}{2} = 8.5 \text{ millimeters} \]
Now we can substitute the value of \( r \) into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times (8.5)^3 \]
Calculating \( (8.5)^3 \):
\[ (8.5)^3 = 614.125 \]
Now we substitute this back into the volume formula:
\[ V = \frac{4}{3} \times 3.14 \times 614.125 \]
Calculating:
\[ V \approx \frac{4}{3} \times 3.14 \times 614.125 \approx \frac{4 \times 3.14 \times 614.125}{3} \]
First, calculate \( 4 \times 3.14 = 12.56 \).
Now calculate \( 12.56 \times 614.125 \):
\[ 12.56 \times 614.125 \approx 7719.07875 \]
Now, divide by 3:
\[ \frac{7719.07875}{3} \approx 2573.02625 \]
Taking this volume into account, it is approximately \( 2573.03 \text{ cubic millimeters} \).
Now, rounding this value, we find that it is closest to option A:
\[ \text{A. } 2,571.14 \text{ cubic millimeters} \]
Thus, the correct choice is:
A. 2,571.14 cubic millimeters.
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