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  • The relative error in the determination of the surface area of a sphere is α. Then the relative error in the determination of its volume is :

The relative error in the determination of the surface area of a sphere is α. Then the relative error in the determination of its volume is :

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Given- Relative error in surface area $\alpha$

To find - Relative error in volume

Solution- Surace area $A = 4\pi r^2$

Relative error in radius  $\frac{\Delta r}{r} = \frac{1}{2} \cdot \frac{\Delta A}{A} = \frac{\alpha}{2}$.

Volume of sphere $V = \frac{4}{3}\pi r^3$

So, relative errors in volume $\frac{\Delta V}{V} = 3 \cdot \frac{\Delta r}{r} = 3 \cdot \frac{\alpha}{2} = \frac{3\alpha}{2}$

Posted by

Saniya Khatri

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