Question

A sphere with a diameter of 13 millimeters

Which measurements is the closest to the volume of the marble in cubic millimeters?

answers:

1,150 mm^3

836 mm^3

6,902 mm 3

9,203 mm34

Answer 1

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.

1. **Calculate the radius**: The radius is half of the diameter. Given that the diameter is 13 millimeters, the radius is:

\[
r = \frac{13}{2} = 6.5 \text{ mm}
\]

2. **Calculate the volume using the formula**:

\[
V = \frac{4}{3} \pi (6.5)^3
\]

3. **Calculate \( (6.5)^3 \)**:

\[
(6.5)^3 = 6.5 \times 6.5 \times 6.5 = 274.625
\]

4. **Substituting into the volume formula**:

\[
V = \frac{4}{3} \pi (274.625)
\]

5. **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**.