Question

What is the approximate volume of the sphere if the surface area is `482.8` `mm^2`?

Answer 1

Volume of sphere is `997.5453` `mm^3`

Explanation:

Surface area `S` of a triangle is given by `4pir^2`, where `r` is radius and volume is given by `4/3pir^3`.

If surface area is `S`, we have `S=4pir^2` or `r^2=S/(4pi)` and `r=1/2sqrt(S/pi)`

and volume of sphere is `4/3pixx(1/2sqrt(S/pi))^3` or `4/3pixxS/(4pi)xx1/2sqrt(S/pi)`

or `S/6sqrt(S/pi)`.

As `S=482.8` and considering `pi=3.1416`,

Volume of sphere is `482.8/6xxsqrt(482.8/3.1416)=482.8/6xx12.397=997.5453` `mm^3`