Related Rates: If r = 12, h = 13, dr/dt = 0.2, dh/dt = 0.5, find dV/dt for right circular cone

[jwag57]

This is a study guide problem and I dont even know where to start with it.

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The volume of a right circular cone of radius r and height h is [math]V(t)\, =\, \frac{\pi}{3}r^2 h.[/math]
Suppose that the radius and height of the cone are changing with respect to time t. At a certain instant of time, the radius and height of the cone are 12 inches and 13 inches, and are increasing at the rate of 0.2 inches/sec and 0.5 inches/sec, respectively. How fast is the volume of the cone increasing?

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Not too much context I can really give seeing as I have no clue how to do it but if there is any further questions for me I would be happy to attempt and answer them

 

[tkhunny]

This is a study guide problem and I dont even know where to start with it.

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The volume of a right circular cone of radius r and height h is [math]V(t)\, =\, \frac{\pi}{3}r^2 h.[/math]
Suppose that the radius and height of the cone are changing with respect to time t. At a certain instant of time, the radius and height of the cone are 12 inches and 13 inches, and are increasing at the rate of 0.2 inches/sec and 0.5 inches/sec, respectively. How fast is the volume of the cone increasing?

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Not too much context I can really give seeing as I have no clue how to do it but if there is any further questions for me I would be happy to attempt and answer them

Can you find the Partial Derivative, [math]\dfrac{\partial V}{\partial r}[/math]?

Can you find the Partial Derivative, [math]\dfrac{\partial V}{\partial h}[/math]?

Can you find the Total Derivative?

Can you make the conceptual leap to Differentials?

 

[Steven G]

This is a study guide problem and I dont even know where to start with it.

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The volume of a right circular cone of radius r and height h is [math]V(t)\, =\, \frac{\pi}{3}r^2 h.[/math]
Suppose that the radius and height of the cone are changing with respect to time t. At a certain instant of time, the radius and height of the cone are 12 inches and 13 inches, and are increasing at the rate of 0.2 inches/sec and 0.5 inches/sec, respectively. How fast is the volume of the cone increasing?

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Not too much context I can really give seeing as I have no clue how to do it but if there is any further questions for me I would be happy to attempt and answer them

They give you the formula for V and ask you how fast is the volume changing when r=12 and h=13. So you need to find dV/dt. This will be in terms of r, h, dr/dt and dh/dt. Now they give you dr/dt and dh/dt by saying that the radius is increasing by .2in per second and that height is increasing by .5 in per second. So plug in the values for r, h, dr/dt and dh/dt into the formula for dV/dt