Question 1 Look up the diameter of you favorite planet with a ring system, then use that diameter to calculate the planet's surface area and volume

1 answer

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:

  1. Surface Area (A) of a sphere:
    \[ A = 4 \pi r^2 \]
    where \( r \) is the radius of the sphere.

  2. 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:

  1. 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.

  2. 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