Question

question 6 (1 point)
convert 454 in³ into cm³ and into ml. (2.54 cm = 1 in).
calculate the final answer in ml.

1
(7.44 x 10³)(------) = 7.44 x 10³

1
1 ml
(7.44 x 10³ cm³)(------) = 7.44 x 10³ ml
1 cm³

Explanation:

Step1: Convert cubic inches to cubic centimeters

We know that \(1\) in \( = 2.54\) cm, so to convert cubic inches to cubic centimeters, we cube the conversion factor. So for \(1\) in\(^3\), the conversion to cm\(^3\) is \((2.54\space\text{cm})^3\) per \(1\space\text{in}^3\).
We have \(454\space\text{in}^3\), so the conversion is \(454\times(2.54)^3\).
First, calculate \((2.54)^3=2.54\times2.54\times2.54 = 16.387064\).
Then \(454\times16.387064\approx454\times16.387 = 454\times16+454\times0.387=7264 + 175.798 = 7439.798\approx7.44\times 10^{3}\space\text{cm}^3\) (this matches the given intermediate step).

Step2: Convert cubic centimeters to milliliters

We know that \(1\space\text{cm}^3 = 1\space\text{mL}\), so the conversion factor from \(\text{cm}^3\) to \(\text{mL}\) is \(\frac{1\space\text{mL}}{1\space\text{cm}^3}\).
So for \(7.44\times 10^{3}\space\text{cm}^3\), when we multiply by \(\frac{1\space\text{mL}}{1\space\text{cm}^3}\), we get \(7.44\times 10^{3}\space\text{mL}\) (since the \(\text{cm}^3\) units cancel out).

Answer:

\(7.44\times 10^{3}\) (or \(7440\))