Who is asking: Student
Level of the question: Secondary

Question: differentiate the volume of a cylinder with V respect to h


Hi there.

I'm not sure where you are stuck on this problem, but to begin it, you need to know how the volume of a cylinder relates to its height. A cylinder is just a circle extruded into the third dimension through a height. Since volume is area times length, all we need is the area of a circle (pi r2) and the height h. So V = pi r2 h.

Now if we assume the radius of the cylinder is held constant and we are just changing the height, we differentiate both sides with respect to h. On the left side, we get dV/dh (which is what the question is asking for) and on the right we have d/dh(pi r2 h). If we are considering r to be constant, then so is r2 and of course pi is a constant, so this equals pi r2 [ d/dh (h)]. I'll leave the last step in the differentiation for you to finish.

Hope this helps,
Stephen La Rocque.