Question

If the percentage error in the measurement of radius of a sphere is 2%, then find the percentage error in the measurement of it's volume​

Answer 1

Given :  Percentage error in radius of sphere = 2 %  

To find :  Percentage error in volume of sphere

Solution :  As we know that,

${\boxed{\sf{Volume \ of \ sphere, \ v = {\dfrac{4}{3}} \pi r^3}}}$

• Expanding it in the language of error -

$\longrightarrow\sf{ {\dfrac{\triangle v}{v}} = 3 {\dfrac{\triangle r}{r}} }$  

•  Multipyling the above expression by 100 to find percentage error.

$\longrightarrow\sf{ {\dfrac{\triangle v}{v}} \times 100 = 3 {\dfrac{\triangle r}{r}} \times 100 }$

$\longrightarrow\sf{ {\dfrac{\triangle v}{v}} \times 100 = 3 \times 2}$

$\longrightarrow\sf{ {\dfrac{\triangle v}{v}} \times 100 = 6}$

Hence, the percentage error in volume of sphere is 6 %.

Answer 2

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Given :  Percentage error in radius of sphere = 2 %  

To find :  Percentage error in volume of sphere

Solution :  As we know that,

${\boxed{\sf{Volume \ of \ sphere, \ v = {\dfrac{4}{3}} \pi r^3}}}$

Expanding it in the language of error -

$\longrightarrow\sf{ {\dfrac{\triangle v}{v}} = 3 {\dfrac{\triangle r}{r}} }$  

 Multipyling the above expression by 100 to find percentage error.

$\longrightarrow\sf{ {\dfrac{\triangle v}{v}} \times 100 = 3 {\dfrac{\triangle r}{r}} \times 100 }$

$\longrightarrow\sf{ {\dfrac{\triangle v}{v}} \times 100 = 3 \times 2}$

$\longrightarrow\sf{ {\dfrac{\triangle v}{v}} \times 100 = 6}$

Hence, the percentage error in volume of sphere is 6 %.