Question

A sphere has a volume of V=2304 in^3. Find its surface area.

Answer 1

The surface area of the sphere is:

`Surface_(sphere)=843.6\,\, in^2`

Explanation:

Recall the two following important formulas:

`Volume_(sphere)=(4)/(3) \,\pi\,\,R^3\\\\Surface_(sphere)=4\,\pi\,R^2`

where R is the radius of the sphere.

Then, since we know the sphere's volume (2304
`in^3`), we can calculate the sphere's radius:

`Volume_(sphere)=(4)/(3) \,\pi\,\,R^3\\2304=(4)/(3) \,\pi\,\,R^3\\(3\,*\,2304)/(4\,\pi) =R^3\\R=\sqrt[3]{(6912)/(4\,\pi) } \, in\\R=8.1934\,\, in`

Now, knowing the radius, we can estimate the surface of the sphere using the other formula;

`Surface_(sphere)=4\,\pi\,R^2\\Surface_(sphere)=4\,\pi\,(8.1934)^2\\Surface_(sphere)=843.6\,\, in^2`