A sphere with a diameter of 13 millimeters

Question

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 mm^3

Answer 1

To find the volume of a sphere, we use the formula:

\[ V = \frac{4}{3} \pi r^3 \]

where \( V \) is the volume and \( r \) is the radius of the sphere.

Given that the diameter of the sphere is 13 millimeters, we can find the radius by dividing the diameter by 2:

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

Now, we can 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 substituting back into the volume formula:

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

Now, calculating \( \frac{4}{3} \times 274.625 \):

\[ \frac{4}{3} \times 274.625 \approx 366.167 \]

Now, calculating the volume with \( \pi \):

\[ V \approx 366.167 \times 3.14159 \approx 1,150.56 \text{ mm}^3 \]

Thus, the closest measurement to the volume of the marble in cubic millimeters is:

1,150 mm³