Question

Calculus Volume Question?

Sketch the region bounded by the curves y=2x√,x+y=3 and y=2/3 then find the volume of the solid generated by revolving this region about the x-axis.

Answer 1

Step 1:

The curve equations are and .

Graph the three curves and .

Observe the graph:

The point of intersection of the three curves are .

Region 1 is bounded by the curves and between .

Region 2 is bounded by the curves and between .

Step 2:

The volume of the solid  is , where is the cross sectional area of the solid .

For region 1:

The outer radius is

The inner radius is .

Integrate under the region .

For region 2:

The outer radius is

The inner radius is .

Integrate under the region .

The volume of region bounded by the curves is 20.47834 cubic units.

Solution:

The volume of region bounded by the curves is 20.47834 cubic units.