Question

In: Math

You plan to calculate the volume of a tall, thin cylinder from measurements of its radius...

You plan to calculate the volume of a tall, thin cylinder from measurements of its radius and height. Which dimension should you measure more carefully? Give reasons for your answer.

Expert Solution

The volume of the cylinder with radius "r" and height "h" is given by

If the error in height is then

Similarly if the error in radius be

Then the error in its volume

Since the product of are smal we can ignore them

Dividing both sids by

Hence the maximum relative error in volume

As we can see the relative error in radius contribute more to relative error in volume

So radius of the wire is to be measured more accurately to minimize the error in Volume.

milcah answered 2 years ago

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