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Sagot :
To convert 36 yards to centimeters, we'll go through the conversion steps one by one.
### Step 1: Convert Yards to Feet
First, we need to convert the length from yards to feet. We know that:
[tex]\[ 1 \text{ yard} = 3 \text{ feet} \][/tex]
For 36 yards:
[tex]\[ 36 \text{ yards} \times 3 \text{ feet per yard} = 108 \text{ feet} \][/tex]
### Step 2: Convert Feet to Inches
Next, we convert the feet to inches. We know that:
[tex]\[ 1 \text{ foot} = 12 \text{ inches} \][/tex]
For 108 feet:
[tex]\[ 108 \text{ feet} \times 12 \text{ inches per foot} = 1296 \text{ inches} \][/tex]
### Step 3: Convert Inches to Centimeters
Finally, we convert the length from inches to centimeters. We know that:
[tex]\[ 1 \text{ inch} = 2.54 \text{ centimeters} \][/tex]
For 1296 inches:
[tex]\[ 1296 \text{ inches} \times 2.54 \text{ centimeters per inch} = 3291.84 \text{ centimeters} \][/tex]
### Summary of Conversion Steps
Combining these steps, we get:
[tex]\[ 36 \text{ yards} \times 3 \text{ feet per yard} \times 12 \text{ inches per foot} \times 2.54 \text{ centimeters per inch} = 3291.84 \text{ centimeters} \][/tex]
This matches the calculation done step-by-step earlier and confirms that the conversion process is correct.
### Identifying the Correct Choice
Given the steps and how they align with the multiple choices provided:
- Option A:
[tex]\[36 \text{ yd} \times \frac{3 \text{ ft}}{1 \text{ yd}} \times \frac{12 \text{ in}}{1 \text{ ft}}\][/tex]
This part correctly converts yards to inches but does not go to centimeters.
- Option B:
[tex]\[36 \text{ yd} \times 3 \text{ ft} \times 12 \text{ in} \times 2.54 \text{ cm}\][/tex]
This choice correctly includes all necessary conversion factors for converting yards to centimeters.
- Option C:
[tex]\[36 \text{ yd} \times \frac{36 \text{ in}}{1 \text{ yd}} \times \frac{2.54 \text{ cm}}{1 \text{ in}}\][/tex]
This incorrectly multiplies the yard by 36 instead of converting foot-inches first.
- Option D:
[tex]\[36 \text{ yd} \times \frac{1 \text{ yd}}{36 \text{ in}} \times \frac{2.54 \text{ cm}}{1 \text{ in}}\][/tex]
This incorrectly attempts to invert the ratio and would give an incorrect conversion.
Thus, the correct selection method from the choices given is [tex]\( \boxed{B} \)[/tex].
### Step 1: Convert Yards to Feet
First, we need to convert the length from yards to feet. We know that:
[tex]\[ 1 \text{ yard} = 3 \text{ feet} \][/tex]
For 36 yards:
[tex]\[ 36 \text{ yards} \times 3 \text{ feet per yard} = 108 \text{ feet} \][/tex]
### Step 2: Convert Feet to Inches
Next, we convert the feet to inches. We know that:
[tex]\[ 1 \text{ foot} = 12 \text{ inches} \][/tex]
For 108 feet:
[tex]\[ 108 \text{ feet} \times 12 \text{ inches per foot} = 1296 \text{ inches} \][/tex]
### Step 3: Convert Inches to Centimeters
Finally, we convert the length from inches to centimeters. We know that:
[tex]\[ 1 \text{ inch} = 2.54 \text{ centimeters} \][/tex]
For 1296 inches:
[tex]\[ 1296 \text{ inches} \times 2.54 \text{ centimeters per inch} = 3291.84 \text{ centimeters} \][/tex]
### Summary of Conversion Steps
Combining these steps, we get:
[tex]\[ 36 \text{ yards} \times 3 \text{ feet per yard} \times 12 \text{ inches per foot} \times 2.54 \text{ centimeters per inch} = 3291.84 \text{ centimeters} \][/tex]
This matches the calculation done step-by-step earlier and confirms that the conversion process is correct.
### Identifying the Correct Choice
Given the steps and how they align with the multiple choices provided:
- Option A:
[tex]\[36 \text{ yd} \times \frac{3 \text{ ft}}{1 \text{ yd}} \times \frac{12 \text{ in}}{1 \text{ ft}}\][/tex]
This part correctly converts yards to inches but does not go to centimeters.
- Option B:
[tex]\[36 \text{ yd} \times 3 \text{ ft} \times 12 \text{ in} \times 2.54 \text{ cm}\][/tex]
This choice correctly includes all necessary conversion factors for converting yards to centimeters.
- Option C:
[tex]\[36 \text{ yd} \times \frac{36 \text{ in}}{1 \text{ yd}} \times \frac{2.54 \text{ cm}}{1 \text{ in}}\][/tex]
This incorrectly multiplies the yard by 36 instead of converting foot-inches first.
- Option D:
[tex]\[36 \text{ yd} \times \frac{1 \text{ yd}}{36 \text{ in}} \times \frac{2.54 \text{ cm}}{1 \text{ in}}\][/tex]
This incorrectly attempts to invert the ratio and would give an incorrect conversion.
Thus, the correct selection method from the choices given is [tex]\( \boxed{B} \)[/tex].
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