The radius of a circular plate is increased by 8%. What will be the approximate percentage increase in its area?

The correct option is 16.64%.

Step 1: Understand the formula for the area of a circular plate.
The area $A$ of a circular plate with radius $r$ is given by the formula:

$A=\pi r^2$

Step 2: Express the new radius after an 8% increase.
Let the initial radius be $r$.
When the radius is increased by 8%, the new radius $r^{\prime }$ becomes:

$r^{\prime }=r+0.08r=1.08r$

Step 3: Calculate the new area.
Substitute the new radius $r^{\prime }$ into the area formula:

$A^{\prime }=\pi {\left(1.08r\right)}^2$

$A^{\prime }=\pi \times 1.1664r^2=1.1664A$

Step 4: Find the percentage increase in area.
The increase in area is:

$\Delta A=A^{\prime }-A=1.1664A-A=0.1664A$

The percentage increase in area is calculated as:

$\text{Percentage Increase}=\left(\frac{0.1664A}{A}\right)\times 100\%=16.64\%$

Thus, the area of the circular plate increases by approximately 16.64%.