Given: A hollow spherical shell having an internal radius of 3cm and external radii of 3.0005 cm
To find: The amount of metal used in the formation of the spherical shell.
Explanation: Let the r and R be the internal and external radii respectively.
So, it is given,
R = 3.0005 and r = 3
Let V be the volume of the hollow shell.
So according to question,
To get the approximate value of , differentiation is carried out
But the integer nearest to 3.0005 is 3,
So 3.0005 = 3+0.0005
So let a = 3 and h = 0.0005
Hence,
Let the function becomes,
Now applying first derivative, we get
Now let
Now we know,
Now substituting the function from (ii) and (iii), we get
Substituting the values of a and h, we get
So, substituting of the value in equation (i),
Hence, the approximate volume of the metal in the hollow spherical shell is .