Question

If curved surface area of a solid sphere is S and volume is V, then find the value of `(S^(3))/V^(2)` [not putting the value of `pi`].

Answer 1

Let the radius of the solid sphere be r unit.
Then the curved surface area of the sphere=`4pir^(2)` sq.units.
As per question, S =`4our^(2)……….` (1)
Also, the volume of the sphere`=(4)/(3)pir^(3)` cu.units.
As per question `V=(4)/(3)pir^(3) ………….`(2)
`therefore (S^(3))/(V^(3))=(4pir^(2))^(3)/((4/3pir^(3))^(2))` [Dividing cube of (1) by square of (2)]=`(64pir^(3)r^(3))/(16/3pir^(2)r^6)=(64xx9)/(16)pi=36pi`
Hence the required value of `S^(3)/(V^(2))=36pi.`