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Calculus Volume Question?

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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.

asked Feb 11, 2015 in CALCULUS by anonymous
reshown Feb 11, 2015 by goushi

1 Answer

0 votes

Step 1:

The curve equations are image and image.

Graph the three curves image and image.

image

Observe the graph:

The point of intersection of the three curves are image.

Region 1 is bounded by the curves image and image between image.

Region 2 is bounded by the curves image and image between image.

Step 2:

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

For region 1:

The outer radius is image

The inner radius is image.

Integrate under the region image.

For region 2:

The outer radius is image

The inner radius is image.

Integrate under the region image.

image

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.

answered Feb 26, 2015 by Lucy Mentor
edited Feb 26, 2015 by Lucy

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