Answer:
[tex]\displaystyle V=\frac{4}{81}\cdot \pi\ cm^3[/tex]
Step-by-step explanation:
The Volume of a Sphere
The volume of a sphere of radius r is given by:
[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot r^3[/tex]
A. )
If the diameter of the sphere is d, the radius is r=d/2. Substituting:
[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot \left (\frac{d}{2} \right )^3[/tex]
Operating
[tex]\displaystyle V=\frac{4}{3}\cdot \pi\cdot \frac{d^3}{8}[/tex]
Simplifying
[tex]\displaystyle V=\frac{1}{6}\cdot \pi\cdot d^3[/tex]
B.)
The diameter of the sphere is 2/3 cm, thus the volume is:
[tex]\displaystyle V=\frac{1}{6}\cdot \pi\cdot \left (\frac{2}{3} \right )^3[/tex]
Operating:
[tex]\displaystyle V=\frac{1}{6}\cdot \pi\cdot \frac{8}{27}[/tex]
[tex]\displaystyle V=\frac{8}{27}\frac{1}{6}\cdot \pi[/tex]
[tex]\boxed{\displaystyle V=\frac{4}{81}\cdot \pi\ cm^3}[/tex]
