Derivation Application in Differential Calculus, verification question problem.

[jamescv31]

Greetings everyone in MHB. :)

Well I've just created a thread to just verify if my answer is correct. On a simple problem that using implicit differentiation.

A cylindrical tank of radius 10 ft is having drained with water at the rate of 200 f^3/ min. How fast is the height of water changed?

Find dh/ dt

My solution goes here:

The formula used is V= (\pi) (r^2) (h)

then substitute the values

200 ft^3/min =pi (100ft) (dh/dt)

therefore my answer is 1/2 pi ft^3/min

Can anyone check this if its a right solution made?

Thanks

 

[Dethrone]

As you correctly surmised, we have:

$$\d{V}{t}=\pi r^2\d{h}{t}$$

The cylindrical tank is being drained, so it's volume is decreasing! $-200 \frac{f^3}{min}$, you have to remember the negative.

Plugging what we know:

$$-200=100\pi \d{h}{t}$$

How can we isolate for $\d{h}{t}$?

 

[jamescv31]

As you correctly surmised, we have:

$$\d{V}{t}=\pi r^2\d{h}{t}$$

The cylindrical tank is being drained, so it's volume is decreasing! $-200 \frac{f^3}{min}$, you have to remember the negative.

Plugging what we know:

$$-200=100\pi \d{h}{t}$$

How can we isolate for $\d{h}{t}$?

by using implicit difference where the -200ft/min is the numerator and the 100 ft is th denominator hence the answer is -1/2 pi ft ^ 3min.

 

[Ackbach]

by using implicit difference where the -200ft/min is the numerator and the 100 ft is th denominator hence the answer is -1/2 pi ft ^ 3min.

$$\frac{-200}{100\pi}=\text{what again?}.$$

Also check your units. The $100\pi$ isn't just $100\pi$. It has some units attached to it, which means your final answer might have different units. What units would make sense?

 

[jamescv31]

its -2 pi ft^3min a typo error. But the implicit difference where the placing of values for numerator and denominator is correct right?