Question

If an error of 2% and 1% are made in measuring height and base radius of a
right circular cylinder then % error in the volume of right circular cylinder is
[Given : Volume of right circular cylinder = ar?h]​

Answer 1

Answer:

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Answer 2

Answer:

The percentage error made in the calculation of volume of the given cylinder is found to be 4%.

Step-by-step explanation:

We are given that the percentage error made in the calculation of height and base radius of the given cylinder is 2% and 1% respectively.

Also, we know that the formula of percentage error in is:

$E(\%)=\frac{\triangle X}{X}\times 100$

where X is the quantity under consideration

Thus, the errors in radius and height can be represented by:

$\frac{\triangle r}{r}\times 100= 1\%$   and

$\frac{\triangle h}{h}\times 100= 2\%$

Also, the formula for calculation of volume of cylinder is:

$V=\pi r^2h$

So, the expression for calculation of error in volume will be:

$\frac{\triangle V}{V}\times 100=2(\frac{\triangle r}{r}\times 100)+\frac{\triangle h}{h}\times 100$

Substituting the errors in radius and height in this expression, we get:

$\frac{\triangle V}{V}\times 100=2(1)+2$

So, we get the error as:

$E(\%)= 4\%$

Thus, the error made in the calculation of Volume will be 4%.