The mass of a planet is [tex]6.2 \times 10^{24}[/tex] kilograms. Its volume is [tex]1.6 \times 10^{12}[/tex] cubic kilometers. Use technology to find the density of the planet (mass/volume) in units of grams per cubic centimeter.

The density of the planet is [tex]\square[/tex] grams per cubic centimeter. (Round to one decimal place as needed.)

We are given that the mass of the planet is
[tex]$$
6.2 \times 10^{24} \text{ kilograms},
$$[/tex]
and its volume is
[tex]$$
1.6 \times 10^{12} \text{ cubic kilometers}.
$$[/tex]

Step 1. Convert the mass to grams

Since
[tex]$$
1 \text{ kilogram} = 1000 \text{ grams},
$$[/tex]
the mass in grams is
[tex]$$
6.2 \times 10^{24} \text{ kg} \times 1000 = 6.2 \times 10^{27} \text{ grams}.
$$[/tex]

Step 2. Convert the volume to cubic centimeters

We know that
[tex]$$
1 \text{ kilometer} = 100000 \text{ centimeters} = 10^5 \text{ cm}.
$$[/tex]
Therefore,
[tex]$$
1 \text{ km}^3 = \left(10^5 \text{ cm}\right)^3 = 10^{15} \text{ cm}^3.
$$[/tex]
Thus, the volume in cubic centimeters is
[tex]$$
1.6 \times 10^{12} \text{ km}^3 \times 10^{15} = 1.6 \times 10^{27} \text{ cm}^3.
$$[/tex]

Step 3. Calculate the density

Density is given by
[tex]$$
\text{density} = \frac{\text{mass}}{\text{volume}}.
$$[/tex]
Substituting the converted values, we have
[tex]$$
\text{density} = \frac{6.2 \times 10^{27} \text{ g}}{1.6 \times 10^{27} \text{ cm}^3}.
$$[/tex]

Dividing the coefficients,
[tex]$$
\frac{6.2}{1.6} \approx 3.875.
$$[/tex]

Step 4. Round the result

Rounding [tex]$3.875$[/tex] to one decimal place gives
[tex]$$
\text{density} \approx 3.9 \text{ g/cm}^3.
$$[/tex]

Thus, the density of the planet is
[tex]$$
\boxed{3.9 \text{ g/cm}^3}.
$$[/tex]