The surface area of sphere is [tex]$67.1\pi \text{ i}{{\text{n}}^{\text{2}}}$[/tex].
What is surface area of sphere?
The area covered by a sphere's outer surface in three-dimensional space is known as its surface area.
The formula of surface area of sphere is,
[tex]$A=4\pi {{r}^{2}}$[/tex]
Where, [tex]A[/tex] is the surface area of sphere, and [tex]r[/tex] is the radius.
It is given that the sphere of volume is [tex]$288\pi \text{ i}{{\text{n}}^{3}}$[/tex].
We have to find the surface area of sphere.
To find the surface area of sphere, we have to find the radius first by using the formula of volume of sphere and then solve for [tex]A[/tex].
So,
The formula for Volume of sphere is,
[tex]$V=\frac{4}{3}\pi {{r}^{3}}$[/tex]
So,
[tex]$3V=4\pi {{r}^{3}}$[/tex]
[tex]${{r}^{3}}=\frac{3V}{4\pi }$[/tex]
[tex]${{r}^{3}}=\frac{3\times 288}{4\pi }$[/tex]
Solve for [tex]r[/tex].
So,
[tex]${{r}^{3}}=68.7549\text{ i}{{\text{n}}^{3}}$[/tex]
Take cube root and simplify it.
[tex]$r=\sqrt[3]{68.7549\text{ i}{{\text{n}}^{3}}}$[/tex]
[tex]$\therefore r=4.0967\text{ in}$[/tex]
Find the surface area by using the formula of surface area of sphere.
So,
[tex]$A=4\pi {{r}^{2}}$[/tex]
[tex]$=4\pi {{\left( 4.0967\text{ in} \right)}^{2}}$[/tex]
[tex]$=4\pi \times 16.2879$[/tex]
[tex]$\therefore A=67.1\pi \text{ i}{{\text{n}}^{2}}$[/tex]
Hence, the surface area of sphere is [tex]$67.1\pi \text{ i}{{\text{n}}^{\text{2}}}$[/tex].
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