Question
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
Answers
GPT-4o mini
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
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