To find the surface area of a sphere, we use the formula:
[tex]\[ \text{Surface Area} = 4 \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere. Given that the radius [tex]\( r \)[/tex] of the planet is 3110 km, we can substitute this value into the formula.
[tex]\[ \text{Surface Area} = 4 \pi (3110)^2 \][/tex]
Calculating [tex]\( (3110)^2 \)[/tex]:
[tex]\[ 3110^2 = 9672100 \][/tex]
Now, substitute this back into the formula:
[tex]\[ \text{Surface Area} = 4 \pi \times 9672100 \][/tex]
Simplify the multiplication:
[tex]\[ \text{Surface Area} = 38688400 \pi \][/tex]
Thus, the exact surface area of the planet is:
[tex]\[ 38688400 \pi \text{ km}^2 \][/tex]
This is the exact answer.
Considering the numerical value of [tex]\( \pi \approx 3.14159 \)[/tex], the surface area of the planet is approximately
[tex]\[ 121543193.21914335 \text{ km}^2 \][/tex]
However, the exact answer remains:
[tex]\[ 38688400 \pi \text{ km}^2 \][/tex]
