What is the surface area of a sphere with a radius of 3 cm?

To find the surface area of a sphere, the formula used is (4\pi r^2), where (r) is the radius of the sphere. In this case, the radius given is 3 cm.

First, we calculate (r^2):

[

r^2 = 3^2 = 9

]

Next, we substitute this value into the surface area formula:

[

\text{Surface Area} = 4\pi r^2 = 4\pi \times 9

]

[

\text{Surface Area} = 36\pi , \text{cm}^2

]

Thus, the surface area of the sphere with a radius of 3 cm is (36\pi , \text{cm}^2). This confirms that the correct answer is aligned with the calculation based on the established formula for the surface area of a sphere.

The other options do not match the computed value, as they either underestimate or miscalculate the relationship between radius and surface area as dictated by the formula.