Question

question 3 (2 points) saved
convert 454 in³ into cm³ and into ml. (2.54 cm = 1 in).
calculate the required conversion factor from 2.54 cm = 1 in.
2.54 cm = 1 in
2.54 cm = 1 in
(2.54 cm)³ = (1 in)³
7.62 cm³ = 1 in³
2.54 cm = 1 in
(2.54)³ = (1)³
16.387 = 1
2.54 cm = 1 in
(2.54 cm)³ = (1 in)³
16.387 cm³ = 1 in³

Explanation:

Step1: Determine the conversion factor for volume

Since we have \(2.54\ \text{cm} = 1\ \text{in}\), to convert cubic inches to cubic centimeters, we cube both sides of the equation. So \((2.54\ \text{cm})^3=(1\ \text{in})^3\).

Step2: Calculate the value of \((2.54)^3\)

Calculating \(2.54\times2.54\times2.54\), we get \(2.54\times2.54 = 6.4516\) and then \(6.4516\times2.54=16.387064\approx16.387\). So \((2.54\ \text{cm})^3 = 16.387\ \text{cm}^3\) and \((1\ \text{in})^3 = 1\ \text{in}^3\), which means \(16.387\ \text{cm}^3 = 1\ \text{in}^3\).

Step3: Convert \(454\ \text{in}^3\) to \(\text{cm}^3\)

Using the conversion factor \(1\ \text{in}^3=16.387\ \text{cm}^3\), we multiply \(454\) by \(16.387\). So \(454\ \text{in}^3\times16.387\ \frac{\text{cm}^3}{\text{in}^3}=454\times16.387\).
Calculating \(454\times16.387\): \(400\times16.387 = 6554.8\), \(50\times16.387 = 819.35\), \(4\times16.387 = 65.548\). Adding them together: \(6554.8+819.35 = 7374.15+65.548 = 7439.698\approx7440\ \text{cm}^3\).

Step4: Convert \(\text{cm}^3\) to \(\text{mL}\)

We know that \(1\ \text{cm}^3 = 1\ \text{mL}\), so \(7439.698\ \text{cm}^3 = 7439.698\ \text{mL}\approx7440\ \text{mL}\).

Answer:

To convert \(454\ \text{in}^3\) to \(\text{cm}^3\) and \(\text{mL}\):

• Conversion factor: \(1\ \text{in}^3 = 16.387\ \text{cm}^3\) (from \((2.54\ \text{cm})^3=(1\ \text{in})^3\) and calculating \((2.54)^3 = 16.387\)).
• \(454\ \text{in}^3\) in \(\text{cm}^3\): \(454\times16.387\approx7440\ \text{cm}^3\).
• \(454\ \text{in}^3\) in \(\text{mL}\): Since \(1\ \text{cm}^3 = 1\ \text{mL}\), it is also approximately \(7440\ \text{mL}\).

For the multiple - choice part, the correct conversion factor derivation is the one with \((2.54\ \text{cm})^3=(1\ \text{in})^3\) and \(16.387\ \text{cm}^3 = 1\ \text{in}^3\) (the last option in the given choices).