Question

question 3 (2 points)
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 correct conversion factor for volume

To convert cubic inches to cubic centimeters, we need to cube the linear conversion factor. Given \(2.54\ \text{cm} = 1\ \text{in}\), cubing both sides gives \((2.54\ \text{cm})^3=(1\ \text{in})^3\).
Calculating \((2.54)^3\): \(2.54\times2.54 = 6.4516\), then \(6.4516\times2.54 = 16.387064\approx16.387\). So \((2.54\ \text{cm})^3 = 16.387\ \text{cm}^3\) and \((1\ \text{in})^3 = 1\ \text{in}^3\), thus \(16.387\ \text{cm}^3 = 1\ \text{in}^3\) is the correct volume conversion factor.

Step2: Convert \(454\ \text{in}^3\) to \(\text{cm}^3\)

Use the conversion factor \(1\ \text{in}^3 = 16.387\ \text{cm}^3\). Multiply \(454\ \text{in}^3\) by the conversion factor: \(454\times16.387\).
Calculating \(454\times16.387\): \(454\times16 = 7264\), \(454\times0.387 = 454\times0.3 + 454\times0.08 + 454\times0.007 = 136.2+36.32 + 3.178 = 175.698\). Then total is \(7264 + 175.698 = 7439.698\approx7440\ \text{cm}^3\).

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

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

Answer:

The correct conversion factor is \( (2.54\ \text{cm})^3=(1\ \text{in})^3 \) leading to \( 16.387\ \text{cm}^3 = 1\ \text{in}^3 \).
\( 454\ \text{in}^3 = 454\times16.387\ \text{cm}^3\approx7440\ \text{cm}^3 \) and \( 7440\ \text{cm}^3 = 7440\ \text{mL} \).

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