Determine the angle swept by the minute hand.

A minute hand completes a full circle ($360^\circ$) in 60 minutes.
The angle swept in 1 minute is:

$$\frac{360^\circ}{60 \text{ minutes}} = 6^\circ/\text{minute}$$

For a stop of 15 minutes, the angle swept ($\theta$) is:

$$\theta = 15 \text{ minutes} \times 6^\circ/\text{minute} = 90^\circ$$

The length of the minute hand is the radius ($r$) of the sector.

$$r = 28 \text{ cm}$$

The formula for the area of a sector is:

$$A = \frac{\theta}{360^\circ} \pi r^2$$

Using $\pi = \frac{22}{7}$, substitute $\theta = 90^\circ$ and $r = 28 \text{ cm}$:

$$A = \frac{90^\circ}{360^\circ} \times \frac{22}{7} \times (28 \text{ cm})^2$$

$$A = \frac{1}{4} \times \frac{22}{7} \times 28 \text{ cm} \times 28 \text{ cm}$$ $$A = \frac{1}{4} \times 22 \times (4 \times 28) \text{ cm}^2$$ $$A = 22 \times 28 \text{ cm}^2$$ $$A = 616 \text{ cm}^2$$

The area swept by the minute hand is $\text{616 cm}^2*$.