Answer:
The surface area of the sphere is [tex]108\pi \sqrt[3]{3}\ in^{2}[/tex]
Step-by-step explanation:
In this problem the volume should be [tex]V=324\pi \ in^{3}[/tex] instead of [tex]V=324\ in^{3}[/tex]
step 1
Find the radius of the sphere
The volume of the sphere is equal to
[tex]V=\frac{4}{3}\pi r^{3}[/tex]
we have
[tex]V=324\pi \ in^{3}[/tex]
substitute and solve for r
[tex]324\pi=\frac{4}{3}\pi r^{3}[/tex]
simplify
[tex]r^{3}=324*3/4[/tex]
[tex]r=\sqrt[3]{243}\ in[/tex]
step 2
Find the surface area of the sphere
The surface area of the sphere is equal to
[tex]SA=4\pi r^{2}[/tex]
we have
[tex]r=\sqrt[3]{243}\ in[/tex]
substitute
[tex]SA=4\pi(\sqrt[3]{243})^{2}[/tex]
simplify
Remember that
[tex](\sqrt[3]{243})^{2}=243^{(2/3)} =27\sqrt[3]{3}[/tex]
[tex]SA=4\pi(27\sqrt[3]{3})=108\pi \sqrt[3]{3}\ in^{2}[/tex]
