If the radius of a sphere is increased by 12 percent, then the volume will be increased by approximately:

The correct answer is 40.49 percent.

Step 1: Understand the formula for the volume of a sphere
The volume $V$ of a sphere of radius $r$ is given by the formula:

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

Step 2: Determine the new radius
Let the initial radius be $r$.
If the radius is increased by 12 percent, the new radius $r^{\prime }$ becomes:

$r^{\prime }=r+0.12r=1.12r$

Step 3: Calculate the new volume
The new volume $V^{\prime }$ is:

$V^{\prime }=\frac{4}{3}\pi {\left(r^{\prime }\right)}^3=\frac{4}{3}\pi {\left(1.12r\right)}^3$

$V^{\prime }=\frac{4}{3}\pi \times 1.404928r^3=1.404928V$

Step 4: Find the percentage increase in volume
The percentage increase in volume is given by:

$\text{Percentage Increase}=\frac{V^{\prime }-V}{V}\times 100$

$\text{Percentage Increase}=\frac{1.404928V-V}{V}\times 100$

$\text{Percentage Increase}=0.404928\times 100=40.4928\%$

Rounding to two decimal places gives approximately 40.49 percent.