# NCERT Class 12-Mathematics: Chapter –6 Application of Derivatives Part 10

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Question 6:

Find the approximate value of .

Given

But the integer nearest to is ,

So,

Hence,

Let the function becomes,

Now applying first derivative, we get

Now

Now we know,

Now substituting the function from (i) and (ii), we get

Substituting the values of a and h, we get

Hence the approximate value of .

Question 7:

Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and , respectively.

Now, we shell use differentiation to get approximate value of

Let

And

Also,

On differentiating both sides we get

Also,

Question 8:

A man, 2m tall, walks at the rate of towards a street light which is above the ground. At what rate is the tip of his shadow moving? At what rate is the length of the shadow changing when he isfrom the base of the light?