Question

How do you find the surface area of the sphere in terms of $\pi $ given $S = 4\pi {r^2}$ and $r = 4.1$cm?

Answer 1

Hint: This problem deals with finding the surface area of the given sphere. Given the radius of the sphere, we have to find the surface area of the given sphere. The surface area of a sphere is the total area covered by its outer surface in three dimensional space. The surface area of any sphere of a radius $r$ is given by:
\[ \Rightarrow S = 4\pi {r^2}\]

Complete step-by-step solution:
Given that the radius of the sphere is equal to 4.1 cm.
The above statement is expressed mathematically, as shown below:
$ \Rightarrow r = 4.1$cm
So now calculating the surface area of the given radius of the sphere.
Here given that we have to find the surface area of the sphere in terms of $\pi $.
That means we do not have to substitute the value of $\pi $ and simplify, but rather just leaving the term $\pi $, as it is, and simplifying the surface area of the sphere.
We know that the surface area of a sphere is given as shown below:
\[ \Rightarrow S = 4\pi {r^2}\]
Now applying this formula to find the surface area of the sphere of radius $r$, 1.4 cm, as shown below:
\[ \Rightarrow S = 4\pi {\left( {4.1} \right)^2}\]
\[ \Rightarrow S = 4\pi \left( {16.81} \right)\]
Now leaving the term $\pi $, and multiplying the numbers 4 and 16.81, as shown:
\[ \Rightarrow S = 67.24\pi \]

The surface area of the sphere is equal to \[67.24\pi \].

Note: Please note that while solving the given above problem we found the surface area of the sphere in terms of $\pi $, as asked, if not we would have multiplied with the value of $\pi $, as we know that the value of $\pi $ is equal to 3.14.