To find the surface area of the sphere with a radius of 7 cm, we can use the surface area formula for a sphere given by
[tex]\[
\text{Surface Area} = 4\pi r^2
\][/tex]
where [tex]\( r \)[/tex] is the radius of the sphere.
1. Identify the radius: We are given that the radius [tex]\( r \)[/tex] is 7 cm.
2. Plug the radius into the formula:
[tex]\[
\text{Surface Area} = 4\pi (7)^2
\][/tex]
3. Calculate the squared radius:
[tex]\[
(7)^2 = 49
\][/tex]
4. Multiply by 4:
[tex]\[
4 \cdot 49 = 196
\][/tex]
5. Multiply by [tex]\(\pi\)[/tex] to express the answer in terms of [tex]\(\pi\)[/tex]:
[tex]\[
196 \pi
\][/tex]
So, the surface area of the sphere is [tex]\( 196\pi \, \text{cm}^2 \)[/tex].
Now, also note that often we calculate the numerical value using [tex]\(\pi \approx 3.14159\)[/tex].
6. Calculate the numerical value:
[tex]\[
196 \pi \approx 196 \times 3.14159 \approx 615.752
\][/tex]
This matches the previously noted result of approximately 615.752.
Therefore, the surface area of the sphere, in terms of [tex]\(\pi\)[/tex], is [tex]\(196\pi \, \text{cm}^2\)[/tex], and numerically it is approximately [tex]\(615.752 \, \text{cm}^2\)[/tex].
