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

1 answer

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:

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

  1. Calculate the volume using the formula:

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

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

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

  1. Substituting into the volume formula:

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

  1. 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.