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Home » Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and 3.0005 cm, respectively.
Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and 3.0005 cm, respectively.
Application of Derivatives | Class 12 | Exercise 1 | Maths | NCERT Exemplar
Find the approximate volume of metal in a hollow spherical shell whose internal and external radii are 3 cm and 3.0005 cm, respectively.

Given,

 

The interior range

    \[r\text{ }=\text{ }3\text{ }cm\]

What’s more, outside sweep

    \[R\text{ }=\text{ }r\text{ }+\text{ }r\text{ }=3.0005\text{ }cm\]

    \[r\text{ }=\text{ }3.0005\text{ }\text{ }3\text{ }=\text{ }0.0005\text{ }cm\]

Let

    \[y\text{ }=\text{ }r3\Rightarrow y\text{ }+\text{ }y\text{ }=\text{ }\left( r\text{ }+\text{ }r \right)3\text{ }=\text{ }R3\text{ }=\text{ }\left( 3.0005 \right)3\]

Separating the two sides w.r.t., r, we get

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 11

 

Consequently, the inexact volume of the metal in the shell is

    \[0.018\pi \text{ }cm3\]

NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 9     NCERT Exemplar Solutions Class 12 Mathematics Chapter 6 - 10

 

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