Question

convert 454 in³ into cm³ and into ml. (2.54 cm = 1 in). put in the units for the conversion factor. in (454 in³)(------------) = cm³ cm in³ (454 in³)(------------) = cm³ cm³ cm (454 in³)(------------) = cm³ in cm³

Explanation:

Step1: Recall volume - unit conversion

We know that $1\mathrm{in}=2.54\mathrm{cm}$. For volume, $(1\mathrm{in})^3=(2.54\mathrm{cm})^3$. So the conversion factor from $\mathrm{in}^3$ to $\mathrm{cm}^3$ is $(2.54)^3\mathrm{cm}^3/\mathrm{in}^3$.

Step2: Convert $454\mathrm{in}^3$ to $\mathrm{cm}^3$

$(454\mathrm{in}^3)\times(2.54^3\frac{\mathrm{cm}^3}{\mathrm{in}^3})=(454)\times(2.54\times2.54\times2.54)\mathrm{cm}^3$.
$2.54^3 = 2.54\times2.54\times2.54=16.387064$.
Then $(454)\times(16.387064)\mathrm{cm}^3 = 7449.727056\mathrm{cm}^3$.
Since $1\mathrm{cm}^3 = 1\mathrm{mL}$, $454\mathrm{in}^3$ is also $7449.727056\mathrm{mL}$.

Answer:

The conversion factor is $(2.54)^3\frac{\mathrm{cm}^3}{\mathrm{in}^3}$, and $454\mathrm{in}^3 = 7449.727056\mathrm{cm}^3=7449.727056\mathrm{mL}$