Sunday

April 20, 2014

April 20, 2014

Posted by **:)** on Monday, May 14, 2012 at 11:49pm.

- Related rates -
**Reiny**, Monday, May 14, 2012 at 11:57pmVolume = V = (1/3)π r^2 h

but h = 2r ---> r = h/2

V = (1/3)π (h^2/4)(h)

= (1/12)π h^3

dV/dt = (1/12)π h^2 dh/dt

10 = 2π (64) dr/dt

dr/dt = 10/(128π) m/min

= 5π/64 m/min

check my arithmetic

- Related rates -
**:)**, Tuesday, May 15, 2012 at 1:24amThank you for answering my question. I just can't understand how it come up to the equation 10=2Π(64)dr/dt. I will be very thankful if you elaborate. :)

- Related rates -
**Reiny**, Tuesday, May 15, 2012 at 8:54amI can see why you are puzzled, since I have two typo errors.

from V = (1/12) π h^3, I should have had ...

**dV/dt = (1/4)π h^2 dh/dt**

now subbing in our given...

10 = (1/4)π(64) dh/dt

10 =16π dh/dt

dh/dt =10/(16π) = 5/(8π) m/min

I apologize for those blatant errors.

- Related rates -
**:)**, Tuesday, May 15, 2012 at 9:30amI'm very thankful for being kind to me. Last one thing, 8 meters is the height of the conical pile. Does it also mean that it is the same as the height of the sand?

- Related rates -
**Reiny**, Tuesday, May 15, 2012 at 10:09amSince we assume that the pile of sand forms a cone,

the height of the cone is equal to height of the sand pile

- Related rates -
**:)**, Tuesday, May 15, 2012 at 7:49pmthank you so much. :) you really help me a lot. Godbless!

- Related rates -
**z**, Tuesday, July 24, 2012 at 6:31amhii... am in the solution with the V = (1/3)π (h^2/4)(h) still have h in 2/4??

isn't the derivative of r = h/2 is just 2/4??

**Related Questions**

related rates calculus problem - A balloon is being filled with air at a rate of...

related rates problem-calculus - A spherical balloon is being filled with air in...

math/unit rate - please help me find the definition for unit rate. It depends ...

calculus: related rates - hello, please help me. A cylindrical can is being ...

calculus(related rates) - Water is leaking out of an inverted conical tank at a ...

Calculus - Related Rates - Bacteria are growing in a circular colony one ...

physics - water at 20°C has viscosity n=1.0*10^-3 Ns/m^2. sand grains have ...

statistics - Investment analysts generally believe the interest rate on bonds is...

Stats - Question 3 Investment analysts generally believe the interest rate on ...

Related Rates - Water is leaking out of an inverted conical tank at a rate of ...