Certainly! Let's find the volume of the Earth using its average radius of 6378 km.
### a) Volume in [tex]\(km^3\)[/tex]
1. Identify the radius: The radius [tex]\(r\)[/tex] of the Earth is 6378 km.
2. Volume of a sphere formula: [tex]\( V = \frac{4}{3} \pi r^3 \)[/tex]
3. Calculation in [tex]\(km^3\)[/tex]:
[tex]\[
V = \frac{4}{3} \pi (6378)^3 \approx 1.087 \times 10^{12} \, km^3
\][/tex]
So, the volume of the Earth in cubic kilometers is [tex]\(1.087 \times 10^{12} \, km^3\)[/tex].
### b) Volume in [tex]\(m^3\)[/tex]
1. Conversion from [tex]\(km^3\)[/tex] to [tex]\(m^3\)[/tex]:
Since [tex]\(1 \, km^3 = 10^9 \, m^3\)[/tex],
[tex]\[
V = 1.087 \times 10^{12} \, km^3 \times 10^9 \, m^3/km^3 \approx 1.087 \times 10^{21} \, m^3
\][/tex]
So, the volume of the Earth in cubic meters is [tex]\(1.087 \times 10^{21} \, m^3\)[/tex].
### c) Volume in [tex]\(mm^3\)[/tex]
1. Conversion from [tex]\(km^3\)[/tex] to [tex]\(mm^3\)[/tex]:
Since [tex]\(1 \, km^3 = 10^{18} \, mm^3\)[/tex],
[tex]\[
V = 1.087 \times 10^{12} \, km^3 \times 10^{18} \, mm^3/km^3 \approx 1.087 \times 10^{30} \, mm^3
\][/tex]
So, the volume of the Earth in cubic millimeters is [tex]\(1.087 \times 10^{30} \, mm^3\)[/tex].
To summarize, the volume of the Earth is:
- [tex]\(1.087 \times 10^{12} \, km^3\)[/tex]
- [tex]\(1.087 \times 10^{21} \, m^3\)[/tex]
- [tex]\(1.087 \times 10^{30} \, mm^3\)[/tex]
