Question

1 When measuring the radius of a sphere an error of 0.6% takes place in the measurement. what is the permissible error while measuring surface areas

Answer 1

Answer:

1 When measuring the radius of a sphere an error of 0.6% takes place in the measurement. what is the permissible error while measuring surface areas

Answer 2

Answer:

The permissible error while measuring the surface area is 1.2%.

Explanation:

Given:

Error in the measurement of radius ($\frac{dr}{r}$) = 0.6%

To find:

Error permissible in the measurement of surface area ($\frac{dA}{A}$)

Formula:

$A=4\pi r^{2}$

Solution:

We know that in the case of exponentials, the errors are multiplied by the power. Therefore,

$\frac{dA}{A}=4\pi (2\frac{dr}{r})$

The constant 4π can be ignored since we are calculating the error. Therefore,

$\frac{dA}{A}= 2\frac{dr}{r}$

$\frac{dA}{A}= 2*0.6%$

$\frac{dA}{A}= 1.2 %$

Therefore, the error in the surface area is 1.2%.

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