To determine the surface area of a sphere, you can use the formula for the surface area of a sphere, which is:
[tex]\[ \text{Surface Area} = 4 \pi r^2 \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the sphere
- [tex]\( \pi \)[/tex] is a mathematical constant approximately equal to 3.14159
Given that the radius [tex]\( r \)[/tex] is 2 meters, we substitute this value into the formula:
[tex]\[ \text{Surface Area} = 4 \pi (2)^2 \][/tex]
Calculate the square of the radius:
[tex]\[ (2)^2 = 4 \][/tex]
Now multiply this result by 4:
[tex]\[ 4 \pi \times 4 \][/tex]
Therefore:
[tex]\[ \text{Surface Area} = 16 \pi \][/tex]
Next, substitute the value of [tex]\(\pi\)[/tex] to get a numerical result. Using [tex]\( \pi \approx 3.14159 \)[/tex]:
[tex]\[ \text{Surface Area} \approx 16 \times 3.14159 \][/tex]
[tex]\[ \text{Surface Area} \approx 50.2655 \][/tex]
Thus, the surface area of the sphere with a radius of 2 meters is approximately 50.2655 square meters.
From the given options, the closest match to 50.2655 is:
B) [tex]\( 50.3 \, m^2 \)[/tex]
So, the correct answer is:
B) [tex]\( 50.3 \, m^2 \)[/tex]
