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Answer :
To convert 18 feet to centimeters, we need to work through the unit conversion process step-by-step. Here’s how you can do it:
1. Understand the Relationship Between Units:
- 1 foot = 12 inches
- 1 inch = 2.54 centimeters
2. Convert Feet to Inches:
- Start by converting feet to inches using the relationship:
[tex]\[
\text{inches} = \text{feet} \times 12
\][/tex]
- For 18 feet:
[tex]\[
\text{inches} = 18 \times 12 = 216 \text{ inches}
\][/tex]
3. Convert Inches to Centimeters:
- Now convert inches to centimeters using the relationship:
[tex]\[
\text{centimeters} = \text{inches} \times 2.54
\][/tex]
- For 216 inches:
[tex]\[
\text{centimeters} = 216 \times 2.54 = 548.64 \text{ centimeters}
\][/tex]
4. Evaluate the Given Options:
- A. Use [tex]\(\frac{12 \text{ in}}{254 \text{ cm}} \times 18 \text{ ft}\)[/tex]
- This is incorrect because it uses a mixed-up conversion factor and does not match the correct conversion process.
- B. Use [tex]\(\frac{254 \text{ cm}}{1 \text{ in}} \times \frac{12 \text{ in}}{1 \text{ ft}} \times 18 \text{ ft}\)[/tex]
- This is correct. It correctly applies the conversion: feet to inches to centimeters.
- C. 18 feet is about 549 cm
- This is correct given the calculated value of 548.64 cm, which rounds to about 549 cm.
- D. 18 feet is about 85 cm
- This is incorrect, as we've calculated 18 feet to be much larger.
- E. [tex]\(1 \text{ ft} = 12\)[/tex] inches
- This statement is correct as per the unit conversion relationship.
Thus, the correct statements for converting 18 feet to centimeters are B, C, and E.
1. Understand the Relationship Between Units:
- 1 foot = 12 inches
- 1 inch = 2.54 centimeters
2. Convert Feet to Inches:
- Start by converting feet to inches using the relationship:
[tex]\[
\text{inches} = \text{feet} \times 12
\][/tex]
- For 18 feet:
[tex]\[
\text{inches} = 18 \times 12 = 216 \text{ inches}
\][/tex]
3. Convert Inches to Centimeters:
- Now convert inches to centimeters using the relationship:
[tex]\[
\text{centimeters} = \text{inches} \times 2.54
\][/tex]
- For 216 inches:
[tex]\[
\text{centimeters} = 216 \times 2.54 = 548.64 \text{ centimeters}
\][/tex]
4. Evaluate the Given Options:
- A. Use [tex]\(\frac{12 \text{ in}}{254 \text{ cm}} \times 18 \text{ ft}\)[/tex]
- This is incorrect because it uses a mixed-up conversion factor and does not match the correct conversion process.
- B. Use [tex]\(\frac{254 \text{ cm}}{1 \text{ in}} \times \frac{12 \text{ in}}{1 \text{ ft}} \times 18 \text{ ft}\)[/tex]
- This is correct. It correctly applies the conversion: feet to inches to centimeters.
- C. 18 feet is about 549 cm
- This is correct given the calculated value of 548.64 cm, which rounds to about 549 cm.
- D. 18 feet is about 85 cm
- This is incorrect, as we've calculated 18 feet to be much larger.
- E. [tex]\(1 \text{ ft} = 12\)[/tex] inches
- This statement is correct as per the unit conversion relationship.
Thus, the correct statements for converting 18 feet to centimeters are B, C, and E.
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