High School

If a sphere has a radius of 2 cm, what is the approximate surface area of the sphere?

A. [tex]$12.1 \, \text{cm}^2$[/tex]
B. [tex]$33.5 \, \text{cm}^2$[/tex]
C. [tex]$50.3 \, \text{cm}^2$[/tex]
D. [tex]$100.5 \, \text{cm}^2$[/tex]

Please select the best answer from the choices provided:
A
B
C
D

Answer :

We start by noting that the formula for the surface area of a sphere is given by

[tex]$$
\text{Surface Area} = 4 \pi r^2,
$$[/tex]

where [tex]$r$[/tex] is the radius of the sphere.

Given that the radius is [tex]$r = 2 \text{ cm}$[/tex], we substitute this value into the formula:

[tex]$$
\text{Surface Area} = 4 \pi (2)^2.
$$[/tex]

Since [tex]$(2)^2 = 4$[/tex], the equation becomes

[tex]$$
\text{Surface Area} = 4 \pi \cdot 4.
$$[/tex]

Multiplying the constants, we get

[tex]$$
\text{Surface Area} = 16 \pi.
$$[/tex]

To find an approximate numerical value, we use [tex]$\pi \approx 3.1416$[/tex]:

[tex]$$
\text{Surface Area} \approx 16 \times 3.1416 \approx 50.2656 \text{ cm}^2.
$$[/tex]

This numerical value is approximately [tex]$50.3 \text{ cm}^2$[/tex]. Among the provided options, the closest match is:

C. [tex]$50.3 \text{ cm}^2$[/tex].