Physics, 30.01.2020 03:56 maxdmontero

About how accurately must the interior diameter of a 10-m high cylindrical storage tank be measured to calculate the tank's volume within 1% of its true value? . about how accurately must the tank's exterior diamter 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?

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Answer from: radom2018

The correct answers are half percentage and 2.5 percentage.

Explanation:

The volume of the cylinder is as follows;

$V=\pi r^{2}h$ ....... (1)

Here, r is the radius and h is the height.

On differentiating on the both side.

$dV=2\pi rhdr$ ........ (2)

Divide (2) by (1).

$\frac{dV}{V}=\frac{2\pi rhdr}{\pi r^{2}h}$

$\frac{dV}{V}=\frac{2dr}{dr}$

$\frac{dr}{r}=\frac{1}{2}\frac{dV}{V}$

Put $\frac{dV}{V}=1%$

$\frac{dr}{r}=\frac{1}{2}1%$

$\frac{dr}{r}=.005$

$\frac{dr}{r}=0.5%$

To get the volume within 1% measure the radius (or the diameter) must be within half percentage of the true radius (or the diameter).

$\frac{dr}{r}=\frac{1}{2}\frac{dV}{V}$

Put $\frac{dV}{V}=5%$

$\frac{dr}{r}=\frac{1}{2}5%$

$\frac{dr}{r}=0.025$

$\frac{dr}{r}=2.5%$

To get the volume within 2.5% measure the radius (or the diameter) must be within half percentage of the true radius (or the diameter).

Answer from: Quest

Ididn’t pass this test sorry

Answer from: Quest

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About how accurately must the interior diameter of a 10-m high cylindrical storage tank be measured...