Respuesta :
Answer: The error of the diameter would be 5% .
Step-by-step explanation:
Since we have given that
[tex]S=2\pi rh[/tex]
Here, r is the radius
h is the height
So, it becomes,
[tex]S=2\pi (\dfrac{D}{2})h\\\\S=\pi Dh\\\\S=\pi D\times 10\\\\S=10\pi D[/tex]
So, we will derivate S wrt D, we get that
[tex]\dfrac{dS}{dD}=10\pi\\\\dS=10\pi dD[/tex]---------------------(1)
As we have given that
it will take to paint the side of the tank to within 5% of the true amount.
So, it becomes,
[tex]dS=0.5\pi D[/tex] ---------------(2)
So, from (1) and (2) , we get that
[tex]0.5\pi D=10\pi dD\\\\\dfrac{0.5\pi}{10\pi}=\dfrac{dD}{D}\\\\0.05=\dfrac{dD}{D}=5\%[/tex]
Hence, the error of the diameter would be 5% .
