Question Convert 1973.1 cubic miles to cubic kilometers using the conversion ratio: $1.61 \mathrm{~km} = 1$ mile.

Studdy Solution

STEP 1

Assumptions
1. The linear conversion ratio is $1.61 \text{ km} = 1 \text{ mile}$ .
2. The volume to be converted is $1973.1 \text{ miles}^3$ .
3. The conversion from miles to kilometers is cubic, meaning we need to cube the linear conversion ratio to convert the volume.

STEP 2

First, we need to establish the linear conversion ratio in terms of kilometers per mile.
$1 \text{ mile} = 1.61 \text{ km}$

STEP 3

To convert a volume from cubic miles to cubic kilometers, we need to cube the linear conversion ratio.
$(1 \text{ mile})^3 = (1.61 \text{ km})^3$

STEP 4

Calculate the cubic conversion ratio.
$(1.61 \text{ km})^3 = 1.61^3 \text{ km}^3$

STEP 5

Compute the value of $1.61^3$ .
$1.61^3 = 1.61 \times 1.61 \times 1.61$

STEP 6

Perform the multiplication to find the cubic conversion ratio.
$1.61^3 = 4.161 \times 1.61 \approx 6.697 \text{ km}^3$

STEP 7

Now that we have the cubic conversion ratio, we can convert the volume from cubic miles to cubic kilometers by multiplying the volume in cubic miles by the cubic conversion ratio.
$\text{Volume in km}^3 = \text{Volume in miles}^3 \times \text{Cubic conversion ratio}$

STEP 8

Plug in the given volume in cubic miles and the cubic conversion ratio to calculate the volume in cubic kilometers.
$\text{Volume in km}^3 = 1973.1 \text{ miles}^3 \times 6.697 \text{ km}^3$

STEP 9

Calculate the volume in cubic kilometers.
$\text{Volume in km}^3 = 1973.1 \times 6.697 \text{ km}^3$

STEP 10

Perform the multiplication to find the volume in cubic kilometers.
$\text{Volume in km}^3 \approx 1973.1 \times 6.697 \approx 13209.7 \text{ km}^3$
The volume is approximately $13209.7 \text{ km}^3$ .

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