Question

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: Use conversion factor for volume

Since \(1\) in \( = 2.54\) cm, then \(1\) in\(^{3}=(2.54)^{3}\) cm\(^{3}\).
\[1\mathrm{in}^{3}=(2.54)^{3}\mathrm{cm}^{3}=16.387064\mathrm{cm}^{3}\]
To convert \(454\) in\(^{3}\) to cm\(^{3}\), we multiply by the conversion - factor:
\[V_{cm^{3}} = 454\times16.387064\mathrm{cm}^{3}\]
\[V_{cm^{3}}=454\times16.387064 = 7449.727056\mathrm{cm}^{3}\approx7.44\times 10^{3}\mathrm{cm}^{3}\]

Step2: Use the relationship between cm\(^{3}\) and mL

We know that \(1\) cm\(^{3}=1\) mL.
To convert the volume from cm\(^{3}\) to mL, we multiply by the conversion factor \(\frac{1\mathrm{mL}}{1\mathrm{cm}^{3}}\).
If \(V = 7.44\times 10^{3}\mathrm{cm}^{3}\), then \(V_{mL}=(7.44\times 10^{3}\mathrm{cm}^{3})\times\frac{1\mathrm{mL}}{1\mathrm{cm}^{3}} = 7.44\times 10^{3}\mathrm{mL}\)

Answer:

\(7.44\times 10^{3}\mathrm{mL}\)