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

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**Question 6:**

Find the approximate value of .

**Answer:**

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.

**Answer:**

Let internal radius and external radius

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?

**Answer:**

Let AB be the street light post and be the height of man

Let

From we see that

On differentiating both sides

Let the distance of the tip of shadow at any instant from the foot of street light is

Hence, the tip of shadow is moving at the rate of towards the light source and length of the shadow is decreasing at the rate of .