Question

The volume of a cylindrical tank is calculated by measuring its height and its diameter. The height and diameter of the tank are measured as 2m and 0.5 m respectively with error of 1% and 2% respectively.find absoulte error and percentage error

Answer 1

Explanation:

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Answer 2

Given: The volume of a cylindrical tank is calculated by measuring its height and its diameter. The height and diameter of the tank are measured as 2 m and 0.5 m respectively with error of 1% and 2% respectively.

To find: The absolute error and percentage error.

Solution:

The volume of a cylinder is given by the formula,

$V = \pi r^{2} h$

   $= \pi (\frac{d}{2} )^{2} h$

Here, V is the volume, r is the radius, d is the diameter of the base and h is the height of the cylinder. As evident from the formula, the volume is directly proportional to the height and the square of the diameter of the cylinder. Now, the absolute error can be calculated as,

$\frac{\delta V}{V} = 2 \frac{\delta d}{d} + \frac{\delta h}{h}$

The value of δd is 2% which is 0.02 and δh is 1% which is 0.01.

$\frac{\delta V}{V} = 2 (\frac{0.02}{5} ) + \frac{0.01}{2}$

    $= 0.013$

The percentage error can be calculated as,

$\frac{\delta V}{V} * 100 = 0.013 * 100$

             $= 1.3$

Therefore, the absolute error is 0.013 and the percentage error is 1.3 %.