To determine the volume of a bubble with a radius of 0.3 mm, we can use the formula for the volume of a sphere:
[tex]\[ V = \frac{4}{3}\pi r^3 \][/tex]
Here, [tex]\( r \)[/tex] is the radius of the sphere. Given [tex]\( r = 0.3 \)[/tex] mm, we will substitute the value of the radius into the volume formula:
[tex]\[ V = \frac{4}{3}\pi (0.3)^3 \][/tex]
First, calculate [tex]\( 0.3^3 \)[/tex]:
[tex]\[ 0.3^3 = 0.3 \times 0.3 \times 0.3 = 0.027 \][/tex]
Now, substitute this result into the volume formula:
[tex]\[ V = \frac{4}{3}\pi \times 0.027 \][/tex]
Next, calculate the multiplication:
[tex]\[ \frac{4}{3} \times 0.027 \][/tex]
[tex]\[ \frac{4}{3} \approx 1.333 \][/tex] (rounded to three decimal places)
[tex]\[ 1.333 \times 0.027 \approx 0.035991 \][/tex]
Finally, multiplying by [tex]\( \pi \approx 3.14159 \)[/tex]:
[tex]\[ V \approx 0.035991 \times 3.14159 \approx 0.113097 \][/tex]
Therefore, the volume of one of these bubbles is approximately 0.113 mm³, which is closest to option A.
So, the correct answer is:
A. about [tex]\(0.11 \, \text{mm}^3\)[/tex]
