- #1

Batmaniac

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I'm stuck on this question:

"A man is sipping soda through a straw from a conical cup, 15 cm deep and 8 cm in diameter at the top. When the soda is 10 cm deep, he is drinking at the rate of 20 cm^3/s. How fast is the level of the soda dropping at that time?"

So you are given height = 15 cm, radius = 4 cm, and the derivative of the volume at height = 10 cm is 20 cm^3/s. It would appear that the question is asking for the derivative of height at 10 cm.

So volume of a cone is 1/3*pi*r^2*h, meaning, the derivative of that is:

dV/dt = (2*pi*r*dr/dt*h)/3 + (dh/dt*pi*r^2)/3

The only problem is that to find dh/dt, as the question is asking, we need to know dr/dt, and I can't think of anything I could do to find it. So perhaps I went about this question the wrong way or there is something I'm not seeing. Any help or guidance would be greatly appreciated, thanks.

"A man is sipping soda through a straw from a conical cup, 15 cm deep and 8 cm in diameter at the top. When the soda is 10 cm deep, he is drinking at the rate of 20 cm^3/s. How fast is the level of the soda dropping at that time?"

So you are given height = 15 cm, radius = 4 cm, and the derivative of the volume at height = 10 cm is 20 cm^3/s. It would appear that the question is asking for the derivative of height at 10 cm.

So volume of a cone is 1/3*pi*r^2*h, meaning, the derivative of that is:

dV/dt = (2*pi*r*dr/dt*h)/3 + (dh/dt*pi*r^2)/3

The only problem is that to find dh/dt, as the question is asking, we need to know dr/dt, and I can't think of anything I could do to find it. So perhaps I went about this question the wrong way or there is something I'm not seeing. Any help or guidance would be greatly appreciated, thanks.

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