The volume of a sphere of radius 4.2 cm is: Use π = $\frac{22}{7}$

The correct answer is 310.464 cm³.

We use the standard formula for the volume of a sphere:

$V=\frac{4}{3}\pi r^3$

Here, the radius $r=4.2$ cm and $\pi =\frac{22}{7}$.

Step 1: Calculate r³

First, find ${\left(4.2\right)}^3$:

$4.2\times 4.2=17.64$

$17.64\times 4.2=74.088$

So, $r^3=74.088$ cm³.

Step 2: Substitute all values into the formula

$V=\frac{4}{3}\times \frac{22}{7}\times 74.088$

Step 3: Multiply the numerators and denominators

Combine the fractions first:

$\frac{4}{3}\times \frac{22}{7}=\frac{4\times 22}{3\times 7}=\frac{88}{21}$

Now multiply by r³:

$V=\frac{88}{21}\times 74.088$

Step 4: Perform the final multiplication

$88\times 74.088=6519.744$

$V=\frac{6519.744}{21}=310.464$

Therefore, the volume of the sphere is 310.464 cm³.