Question

A glass marble has a diameter of 17 millimeters. What is the approximate volume of the marble? Use 3.14 for .
A.
2,571.14 cubic millimeters
B.
302.49 cubic millimeters
C.
20,569.09 cubic millimeters
D.
1,209.95 cubic millimeters

Answer 1

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**.