Sure, let's work through the problem step-by-step to find the rate at which the area is increasing in square meters per minute.
1. Understanding the rate in square feet per hour:
- The problem states that the area is increasing at a rate of 20 square feet per hour.
2. Converting square feet to square meters:
- We know that 1 meter (m) is approximately equal to 3.2 feet (ft).
- Therefore, to convert an area from square feet to square meters, we need to account for the conversion in both dimensions (length and width).
- Hence, the conversion factor from square feet to square meters is [tex]\((3.2 \text{ ft})^2 = 3.2^2 = 10.24\)[/tex].
- To convert from square feet to square meters, we divide by the conversion factor: [tex]\( \frac{1 \text{ square foot}}{10.24} \)[/tex].
- Therefore, 20 square feet per hour is equivalent to [tex]\( \frac{20}{10.24} \)[/tex] square meters per hour.
3. Calculating the rate in square meters per hour:
- [tex]\( \frac{20}{10.24} \approx 1.953125 \)[/tex] square meters per hour.
4. Converting the rate to square meters per minute:
- Since there are 60 minutes in an hour, we need to divide the rate in square meters per hour by 60 to get the rate in square meters per minute.
- [tex]\( \frac{1.953125 \text{ square meters per hour}}{60} \approx 0.0325520833 \)[/tex] square meters per minute.
5. Comparing with the given options:
- Given our calculation, the rate of increase in square meters per minute is approximately 0.0326.
- Among the options provided:
- A) 0.03
- B) 0.10
- C) 1.09
- D) 200
- The closest option to 0.0326 is A) 0.03.
Therefore, the closest rate in square meters per minute is option A) 0.03.
