Final answer:
The patch's area in square kilometers is 1.88 x 10^-9 km², and the cost of the patch is $2.2 (to the nearest 10th).
Step-by-step explanation:
To find the patch's area in square kilometers, we need to convert the volume of the patch into square centimeters. Since 1 cm = 10^-5 km, the volume of the patch in cm³ is 18.8 cm³. To convert it to km², we divide by 10^10. So, the patch's area in square kilometers is 18.8 cm³ / 10^10 = 1.88 x 10^-9 km².
To calculate the cost of the patch, we need to know the cost per cm². Since the area of the patch is 18.8 cm³, and the cost is $4.10, we divide the cost by the area to get the cost per cm². The cost per cm² is $4.10 / 18.8 cm² = $0.2181 per cm². Since the patch's area is in km², we multiply the cost per cm² by 10^10 to get the cost per km². The cost per km² is $0.2181 x 10^10 = $2.181 x 10^9. Rounded to the nearest 10th, the cost of the patch is $2.2 (to the nearest 10th).