# Thread: work,volume problem

1. ## work,volume problem

Consider the region bounded by y=x^3 +24x^2 + 192x 0<=x<=2 on the left, by x axis along the bottom, by the line y=488 along the top, and by the line x=4 along the right. Suppose the region is revolved around the line x=8 to produce a solid of revolution. Find the network done in turning this solid upside down. Assume that the solid is made of a metal alloy whose density is 9200 kg/m^3 and units are meters. Express answer in Joules.

My first question is what od they mean by turning it upside down. FLipping it so it's underneath the x-axis? Where do I go from there?

2. Originally Posted by sheridan
Consider the region bounded by y=x^3 +24x^2 + 192x 0<=x<=2 on the left, by x axis along the bottom, by the line y=488 along the top, and by the line x=4 along the right. Suppose the region is revolved around the line x=8 to produce a solid of revolution. Find the network done in turning this solid upside down. Assume that the solid is made of a metal alloy whose density is 9200 kg/m^3 and units are meters. Express answer in Joules.

My first question is what od they mean by turning it upside down. FLipping it so it's underneath the x-axis? Where do I go from there?
(no not flipping it so its under the x-axis but flipping it then moving it back up so that its lower edge is on the x axis)

Calculate the center of mass $\displaystyle c=(x_c,y_c)$ , and the mass $\displaystyle m$ of the solid.

Then the work done in flipping it upside down is the change in potential energy when a mass $\displaystyle m$ is moved from $\displaystyle (x_c, y_c)$ to $\displaystyle (x_c,488-y_c).$

Which is $\displaystyle mg(488-2y_c)$

RonL