Question

About how accurately must the tank's exterior diameter be measured to calculate the amount of paint it will take to paint the side of the tank to within 5% of the true amount? Express your answer as a percentage of the outer diameter:

Answer 1

Answer: The error of the diameter would be 5% .

Explanation:

Since we have given that

`S=2\pi rh`

Here, r is the radius

h is the height

So, it becomes,

`S=2\pi ((D)/(2))h\\\\S=\pi Dh\\\\S=\pi D* 10\\\\S=10\pi D`

So, we will derivate S wrt D, we get that

`(dS)/(dD)=10\pi\\\\dS=10\pi dD`---------------------(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,

`dS=0.5\pi D` ---------------(2)

So, from (1) and (2) , we get that

`0.5\pi D=10\pi dD\\\\(0.5\pi)/(10\pi)=(dD)/(D)\\\\0.05=(dD)/(D)=5\%`

Hence, the error of the diameter would be 5% .