Question

question 4 (2 points)
convert 454 in³ into cm³ and into ml. (2.54 cm = 1 in).
put in the numbers for the conversion factor.
1 cm³
(454 in³)(----------) = cm³
16.387 in³
16.387 cm³
(454 in³)(----------) = cm³
1 in³

Explanation:

Step1: Find the conversion factor for volume

Since \(1\ \text{in} = 2.54\ \text{cm}\), then \(1\ \text{in}^3=(2.54\ \text{cm})^3 = 2.54\times2.54\times2.54\ \text{cm}^3\approx16.387\ \text{cm}^3\). So the conversion factor from \(\text{in}^3\) to \(\text{cm}^3\) is \(\frac{16.387\ \text{cm}^3}{1\ \text{in}^3}\).

Step2: Set up the conversion

We have \(454\ \text{in}^3\), and we multiply by the conversion factor \(\frac{16.387\ \text{cm}^3}{1\ \text{in}^3}\) to get \(\text{cm}^3\). So the blank should be \(\frac{16.387\ \text{cm}^3}{1\ \text{in}^3}\), and then \(454\ \text{in}^3\times\frac{16.387\ \text{cm}^3}{1\ \text{in}^3}=454\times16.387\ \text{cm}^3\approx7439.7\ \text{cm}^3\) (but for the conversion factor part, we just need to identify the correct factor).

Answer:

The correct conversion factor is \(\frac{16.387\ \text{cm}^3}{1\ \text{in}^3}\), so the second option's blank is filled with \(\frac{16.387\ \text{cm}^3}{1\ \text{in}^3}\) and the calculation would be \(454\times16.387 = 7439.708\ \text{cm}^3\) (and since \(1\ \text{cm}^3 = 1\ \text{mL}\), it is also \(7439.708\ \text{mL}\)). For the conversion factor in the problem, the correct one is \(\frac{16.387\ \text{cm}^3}{1\ \text{in}^3}\) (the second option's numerator and denominator as \(\frac{16.387\ \text{cm}^3}{1\ \text{in}^3}\)).