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% .

Step-by-step explanation:

Since we have given that

$S=2\pi rh$

Here, r is the radius

h is the height

So, it becomes,

$S=2\pi (\dfrac{D}{2})h\\\\S=\pi Dh\\\\S=\pi D\times 10\\\\S=10\pi D$

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

$\dfrac{dS}{dD}=10\pi\\\\dS=10\pi dD$---------------------(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

$0.5\pi D=10\pi dD\\\\\dfrac{0.5\pi}{10\pi}=\dfrac{dD}{D}\\\\0.05=\dfrac{dD}{D}=5\%$

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