One of my favorite planets with a ring system is Saturn. The diameter of Saturn is approximately 120,536 kilometers.
To calculate the surface area and volume of a planet, we can use the following formulas:
-
Surface Area (A) of a sphere:
\[ A = 4 \pi r^2 \]
where \( r \) is the radius of the sphere. -
Volume (V) of a sphere:
\[ V = \frac{4}{3} \pi r^3 \]
First, we need to find the radius. The radius \( r \) is half of the diameter:
\[ r = \frac{\text{Diameter}}{2} = \frac{120,536 \text{ km}}{2} = 60,268 \text{ km} \]
Now we can calculate the surface area and volume:
-
Surface Area:
\[ A = 4 \pi (60,268 \text{ km})^2 \]
\[ A \approx 4 \pi (3,628,270,784 \text{ km}^2) \]
\[ A \approx 4 \times 3.14159 \times 3,628,270,784 \text{ km}^2 \]
\[ A \approx 45,258,888,690 \text{ km}^2 \]
So, the surface area of Saturn is approximately 45.26 million square kilometers. -
Volume:
\[ V = \frac{4}{3} \pi (60,268 \text{ km})^3 \]
\[ V \approx \frac{4}{3} \pi (219,452,672,961,352 \text{ km}^3) \]
\[ V \approx \frac{4}{3} \times 3.14159 \times 219,452,672,961,352 \text{ km}^3 \]
\[ V \approx 919,963,846,042,204 \text{ km}^3 \]
So, the volume of Saturn is approximately 919.96 million cubic kilometers.
In summary:
- Surface Area of Saturn: ~45.26 million km²
- Volume of Saturn: ~919.96 million km³