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Good evening Annela!!! Here are my workings for Q7.
Date Posted:
4 years ago
Can i ask why you can use area of cylinder to find rate of flow? I thought it should cm^3 /seconds so find dv/dt ?
The first part, apparently, goes like this.
Water is added to the cylinder at a constant rate to be found.
We know that a cylinder’s circular cross-section area at all heights of the cylinder are the same. So, the increase in volume has to be proportional to the increase in height, since the increase in height is a constant.
Because we know that the height increase is a fixed constant at k cm per second, the volume increase must also be fixed throughout.
For this reason, we can use the method above. We cannot use such methods when the cross sectional area changes at different height levels (for example in a cone or in a hemisphere), since the volume increase will not be constant if the height increase is constant, or vice versa.
In one second, the increase in height is k cm. So the increase in volume of water must be pi r2 k since the cross sectional area is a circle of diameter 10 cm.
Hence, dV/dt = pi * 5^2 * k.
Remember that dV/dt measures the rate of change of volume ie how much the volume changes in one second.
Water is added to the cylinder at a constant rate to be found.
We know that a cylinder’s circular cross-section area at all heights of the cylinder are the same. So, the increase in volume has to be proportional to the increase in height, since the increase in height is a constant.
Because we know that the height increase is a fixed constant at k cm per second, the volume increase must also be fixed throughout.
For this reason, we can use the method above. We cannot use such methods when the cross sectional area changes at different height levels (for example in a cone or in a hemisphere), since the volume increase will not be constant if the height increase is constant, or vice versa.
In one second, the increase in height is k cm. So the increase in volume of water must be pi r2 k since the cross sectional area is a circle of diameter 10 cm.
Hence, dV/dt = pi * 5^2 * k.
Remember that dV/dt measures the rate of change of volume ie how much the volume changes in one second.
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Good evening Annela! Here are my workings for Q8.
Date Posted:
4 years ago