Answer :
To solve this problem, we need to convert 1.00 cubic centimeter (cm³) to cubic inches (in³).
We start with the given conversion factor:
[tex]\[ 1 \text{ inch} = 2.54 \text{ cm} \][/tex]
Since we are dealing with volume, we need to cube this conversion factor because we are converting cubic centimeters to cubic inches:
[tex]\[ 1 \text{ cm}^3 = \left(\frac{1 \text{ inch}}{2.54 \text{ cm}}\right)^3 \][/tex]
Next, we calculate the conversion factor for the volume:
[tex]\[ \left(\frac{1 \text{ inch}}{2.54 \text{ cm}}\right)^3 = \left(\frac{1}{2.54}\right)^3 \text{ inch}^3 \][/tex]
We find the cubed value of [tex]\( \frac{1}{2.54} \)[/tex]:
[tex]\[ \left(\frac{1}{2.54}\right)^3 \approx 0.061023744094732275 \text{ inch}^3 \][/tex]
Therefore,
[tex]\[ 1.00 \text{ cm}^3 \approx 0.061023744094732275 \text{ inch}^3 \][/tex]
Now, we compare this value to the given choices:
A. [tex]\(0.155 \text{ in}^3 \)[/tex]
B. [tex]\(0.0610 \text{ in}^3 \)[/tex]
C. [tex]\(0.394 \text{ in}^3 \)[/tex]
D. [tex]\(6.45 \text{ in}^3 \)[/tex]
E. [tex]\(16.4 \text{ in}^3 \)[/tex]
The closest value to 0.061023744094732275 in³ is [tex]\(0.0610 \text{ in}^3\)[/tex].
Thus, the correct answer is:
B. [tex]\(0.0610 \text{ in}^3 \)[/tex].
We start with the given conversion factor:
[tex]\[ 1 \text{ inch} = 2.54 \text{ cm} \][/tex]
Since we are dealing with volume, we need to cube this conversion factor because we are converting cubic centimeters to cubic inches:
[tex]\[ 1 \text{ cm}^3 = \left(\frac{1 \text{ inch}}{2.54 \text{ cm}}\right)^3 \][/tex]
Next, we calculate the conversion factor for the volume:
[tex]\[ \left(\frac{1 \text{ inch}}{2.54 \text{ cm}}\right)^3 = \left(\frac{1}{2.54}\right)^3 \text{ inch}^3 \][/tex]
We find the cubed value of [tex]\( \frac{1}{2.54} \)[/tex]:
[tex]\[ \left(\frac{1}{2.54}\right)^3 \approx 0.061023744094732275 \text{ inch}^3 \][/tex]
Therefore,
[tex]\[ 1.00 \text{ cm}^3 \approx 0.061023744094732275 \text{ inch}^3 \][/tex]
Now, we compare this value to the given choices:
A. [tex]\(0.155 \text{ in}^3 \)[/tex]
B. [tex]\(0.0610 \text{ in}^3 \)[/tex]
C. [tex]\(0.394 \text{ in}^3 \)[/tex]
D. [tex]\(6.45 \text{ in}^3 \)[/tex]
E. [tex]\(16.4 \text{ in}^3 \)[/tex]
The closest value to 0.061023744094732275 in³ is [tex]\(0.0610 \text{ in}^3\)[/tex].
Thus, the correct answer is:
B. [tex]\(0.0610 \text{ in}^3 \)[/tex].
