Question

a chevy v - 8 engine displaces 454 in³. calculate the displacement in l, (2.54 cm = 1 in). the conversion factor between in³ and cm³ is numerically, without units 1. the conversion factor between cm³ and ml is numerically, without units 2. the conversion factor between ml and l is numerically, without units 3. the final answer is 4 l. a. 2.54 = 1 b. 6.452 = 1 c. 16.387 = 1 d. 1 = 1 e. 10³ = 1 f. 7.44 x 10³ g. 7.44 h. 27.7 i. 2.93 x 10³ j. 2.93 k. 293 l. 1.15 x 10³ m. 115

Explanation:

Step1: Find conversion from in³ to cm³

Since \(1\ in = 2.54\ cm\), then \(1\ in^{3}=(2.54)^{3}\ cm^{3}=16.387\ cm^{3}\), so the conversion factor from \(in^{3}\) to \(cm^{3}\) is \(16.387 = 1\) (in the sense of the ratio for conversion).

Step2: Recall cm³ - mL conversion

By definition, \(1\ cm^{3}=1\ mL\), so the conversion factor is \(1 = 1\).

Step3: Recall mL - L conversion

We know that \(1\ L = 1000\ mL\), so the conversion factor is \(10^{3}=1\).

Step4: Convert 454 in³ to L

\[454\ in^{3}\times\frac{16.387\ cm^{3}}{1\ in^{3}}\times\frac{1\ mL}{1\ cm^{3}}\times\frac{1\ L}{1000\ mL}=7.44\ L\]

Answer:

1. C. \(16.387 = 1\)
2. D. \(1 = 1\)
3. E. \(10^{3}=1\)
4. G. \(7.44\)