Identify Given Values

The radius $r$ is given as $3.5$ cm, which can be written as the fraction $\frac{7}{2}$ cm to simplify calculations.

$r = \frac{7}{2} \text{ cm}$

Apply Volume Formula

Substitute $r = \frac{7}{2}$ and $\pi = \frac{22}{7}$ into the volume formula for a sphere: $V = \frac{4}{3} \pi r^3$.

$V = \frac{4}{3} imes \frac{22}{7} imes \left(\frac{7}{2}\right)^3$

Perform Calculation

Expand the cube: $(\frac{7}{2})^3 = \frac{343}{8}$. Now calculate $V = \frac{4}{3} imes \frac{22}{7} imes \frac{343}{8}$.

$V = \frac{4 imes 22 imes 343}{3 imes 7 imes 8} = \frac{11 imes 49}{3} = \frac{539}{3}$

Final Division

Dividing $539$ by $3$ gives the final volume of approximately $179.666...$, which rounds to $179.67$.

$V \approx 179.67 \text{ cm}^3$