This once again is a small change approximation question, just used in a different way.
It is first crucial to understand what they're asking for. The company likes to produce spheres with volume of
, however the volume can exceed or go below this value by
. We usually call this the 'error margin' as in reality we can't produce a sphere of exact volume all the time, there will be some variation, usually expressed as
. Our goal in this problem is to work out the the radius and its error margin, expressed as
I'll give you pointers to work out the rest. Given the volume of
, find the radius first, finding
.
To find the error margin of the radius, this is where small change approximation comes in handy where:
In this case
and
represents the error margin in the small change approximation formula. The reason we can use this is that we are looking at the variation of
when
is allowed to change within its error margin.
Hope this help, finding error margin is just another application of small change approximation in differentiation, pretty cool eh?
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