Answer :
Final answer:
The temperature ranges in Celsius for the given Fahrenheit ranges are approximately: a) 98.89°C to 104.44°C, b) 104.44°C to 110°C, c) 110°C to 115.56°C, d) 115.56°C to 121.11°C
Explanation:
The temperature range in Celsius for the given Fahrenheit range can be calculated using the formula ATF = ATC. This means that a temperature difference of one degree on the Celsius scale is 1.8 times as large as a difference of one degree on the Fahrenheit scale. Therefore, to find the Celsius range for each Fahrenheit range, we can multiply the Fahrenheit range by 5/9. Let's calculate the temperature range for each option:
- a) 210-220: \(\frac{{210-32}}{{1.8}}\) to \(\frac{{220-32}}{{1.8}}\) which is approximately 98.89°C to 104.44°C
- b) 220-230: \(\frac{{220-32}}{{1.8}}\) to \(\frac{{230-32}}{{1.8}}\) which is approximately 104.44°C to 110°C
- c) 230-240: \(\frac{{230-32}}{{1.8}}\) to \(\frac{{240-32}}{{1.8}}\) which is approximately 110°C to 115.56°C
- d) 240-250: \(\frac{{240-32}}{{1.8}}\) to \(\frac{{250-32}}{{1.8}}\) which is approximately 115.56°C to 121.11°C
Learn more about Temperature Conversion here:
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The answer is as follows:
To convert Fahrenheit (F) to Celsius (C), we use the formula:
[tex]\( C = \frac{5}{9}(F - 32) \)[/tex]
Let's perform the conversions for each range, following this formula:
For the range 210-220°F:
Lower bound: (210 - 32) * 5/9 = 178/9 ≈ 19.78°C
Upper bound: (220 - 32) * 5/9 = 188/9 ≈ 20.89°C
For the range 220-230°F:
Lower bound: (220 - 32) * 5/9 = 188/9 ≈ 20.89°C
Upper bound: (230 - 32) * 5/9 = 198/9 ≈ 22.00°C
For the range 230-240°F:
Lower bound: (230 - 32) * 5/9 = 198/9 ≈ 22.00°C
Upper bound: (240 - 32) * 5/9 = 208/9 ≈ 23.11°C
For the range 240-250°F:
Lower bound: (240 - 32) * 5/9 = 208/9 ≈ 23.11°C
Upper bound: (250 - 32) * 5/9 = 218/9 ≈ 24.22°C
Therefore, the temperature ranges in Celsius for the given Fahrenheit ranges are:
a) Approximately 19.78°C to 20.89°C
b) Approximately 20.89°C to 22.00°C
c) Approximately 22.00°C to 23.11°C
d) Approximately 23.11°C to 24.22°C
