Revolution of a curve along a axis

kazthehack
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Homework Statement


given z =y3 revolved around the y-axis what is the equation of the surface and then graph.


Homework Equations





The Attempt at a Solution


I have no idea how to approach this, i tried searching around the net but nothing came out. pls help.
 
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start with the equation of a circle of radius z = y^3, with centre on the y-axis & in a plane perpindicular to the y axis
 
^ what i need is a step by step solution and i learn to solve other problems if i see how it is done.
 
sorry, you have to try - I'm happy to walk you through it if you attempt, but I'm not just going to do it all for you
 
kazthehack said:
given z =y3 revolved around the y-axis what is the equation of the surface and then graph.

I have no idea how to approach this, i tried searching around the net but nothing came out. pls help.

Hi kazthehack! :wink:

Start with a single point z =y03 (for a fixed value y0) revolved around the y-axis …

what is the equation of that? :smile:
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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