To find the volume of a sphere with a given radius, we use the formula for the volume of a sphere, which is
[tex]\[ V = \frac{4}{3} \pi r^3 \][/tex]
Given the radius [tex]\( r \)[/tex] is 6 mm, let's substitute [tex]\( r \)[/tex] with 6 in the formula.
[tex]\[ V = \frac{4}{3} \pi (6)^3 \][/tex]
First, calculate [tex]\( (6)^3 \)[/tex]:
[tex]\[ 6^3 = 6 \times 6 \times 6 = 216 \][/tex]
Next, multiply this result by [tex]\( \frac{4}{3} \)[/tex]:
[tex]\[ \frac{4}{3} \times 216 = 4 \times \frac{216}{3} = 4 \times 72 = 288 \][/tex]
So, the volume in terms of [tex]\( \pi \)[/tex] would be:
[tex]\[ V = 288 \pi \text{ mm}^3 \][/tex]
Thus, the volume of the sphere with radius 6 mm is:
[tex]\[ V = 288 \pi \text{ mm}^3 \][/tex]
Which aligns with the result we used.
