Answer:
6%
Step-by-step explanation:
A function f(x) can by approximated at and around a point, say x = a by,
f(x) = f(a) + f'(a)(x-a)
where, [tex]f'(x)=\frac{df}{dx}[/tex]
Here, volume V is a function of radius r and height h. In the 2 dimensional case, we have to take the partial derivatives.
Given,
[tex]V=\pi r^2h[/tex]
or, [tex]dV=\frac{\partial V }{\partial r}dr+ \frac{\partial V }{\partial h}dh[/tex]
at r = 1.55 m and h = 6.6 m
[tex]dr=0.02\times1.55m=0.031m[/tex]
[tex]dh=0.02\times6.6m=0.132m[/tex]
[tex]\frac{\partial V }{\partial r}=2\pi r h=2\pi \times 1.55\times 6.6=64.277[/tex]
[tex]\frac{\partial V }{\partial h}=\pi r^2=7.5477[/tex]
Therefore, [tex]dV=(64.277\times.031)+(7.5477\times0.132)=2.9889m[/tex]
Also, [tex]V=\pi r^2h=49.8147m[/tex]
Hence, maximum error is given by,
[tex]R=\frac{2.9889}{49.8147} \times 100[/tex]
= 6%
