(a) The actual area of a reservoir is \( 3.875 \mathrm{~km}^{2} \). The scale of Map \( A \) is \( 1: 25000 \). Find the area of the reservoir, in \( \mathrm{cm}^{2} \), on Map \( A \).

To find the area of the reservoir on Map \( A \), we start with the actual area of the reservoir, which is \( 3.875 \, \text{km}^2 \). To convert this area from square kilometers to square centimeters, we use the conversion factor that \( 1 \, \text{km}^2 = 10^8 \, \text{cm}^2 \). So, \[ 3.875 \, \text{km}^2 = 3.875 \times 10^8 \, \text{cm}^2 = 387500000 \, \text{cm}^2. \] Next, we apply the scale of the map, which is \( 1:25000 \). This means that \( 1 \, \text{cm} \) on the map represents \( 25000 \, \text{cm} \) in reality. To find the area on the map, we square the scale factor: \[ \left(\frac{1}{25000}\right)^2 = \frac{1}{625000000} \, \text{cm}^2/\text{cm}^2. \] Now, we multiply the actual area in square centimeters by the scale factor: \[ \text{Area on Map A} = 387500000 \, \text{cm}^2 \times \frac{1}{625000000} = \frac{387500000}{625000000} \, \text{cm}^2. \] Calculating this gives: \[ \text{Area on Map A} = 0.620 \, \text{cm}^2. \] Therefore, the area of the reservoir on Map \( A \) is approximately \( 0.620 \, \text{cm}^2 \).