Volume, moment, mass of solid of revolution

[kate45]

Hi there,

I have no idea about this question can anyone help?

S is a solid of revolution in 3-dimensions, formed by rotating a full turn about the y-axis, the region in the first quadrant of the (x, y)-plane bounded by the interval [1, 2] on the y-axis, and the curve x = (2 − y)(y − 1)^2

(a) Find the volume, moment My and centre of mass of the solid ob ject S .
(b) Formulate as an integral, but do not evaluate, the surface area of solid S.

 

[Defennder]

You said you have no idea how to do the questions. Have you learned the general triple integral formulae for evaluating centre of mass, moments? And do you know how to find the surface area generated by a revolving curve?

 

[kate45]

HI,

I think i need to find A(y) which equals pi(2-y)(y-1)^2

then integrate this with respect to the intervals 1 and 2 which then gives the volume?

the moment and centre of mass, plus that last section i am stuck on