Hello Can someone please help me out with the following qustion...
The radius of a Cylinder is reduced by 4% and its height is increased by 2%
(a)Determine the approximate change in the cylinders volume
(b)Determine the curved surface area (volume = pi r(squared)h and curved surface area = 2pi rh)
hi Chris,
the radius being reduced by 4% causes the radius to decrease by 0.04 of it's original length,
as 4% is
Therefore, the new radius length can still be expressed using the old radius by writing
the height increases by 2%, so the new height is h+2% of h
Since the original problem said "approximate", I wonder if this isn't for a Calculus class!
so
Then
"dr/r" is approximately -4%= -.04, "dh/h" is approximately +2%= +.02, so, approximately, dV/V= 2(-.04)+ .02= -.06.
This differs from what you would get using the others' method because it does not include the products of the percents multiplied together.
This is the same as the old mechanics rule of thumb: "When quantities are added, their errors add; when quantities are multiplied, their relative errors add." Here we have "r*r*h". Their "relative errors" are -.04 and .02 so the relative error in V is -.04- .04+ .02.