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6.3 Shell Method. HW pg 432 2-10, 14 (even). Find the volume of the region bounded by , , and revolved about the y -axis. We can use the washer method if we split it into two parts:. cylinder. inner radius. outer radius. thickness of slice.

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6 3 shell method

6.3 Shell Method

HW pg 432 2-10, 14 (even)


Find the volume of the region bounded by , , and revolved about the y-axis.

We can use the washer method if we split it into two parts:

cylinder

inner

radius

outer

radius

thickness

of slice

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Here is another way we could approach this problem: , and revolved about the

cross section

If we take a vertical slice

and revolve it about the y-axis

we get a cylinder.

If we add all of the cylinders together, we can reconstruct the original object.


cross section , and revolved about the

The volume of a thin, hollow cylinder is given by:

r is the x value of the function.

h is the y value of the function.

thickness is dx.


This is called the , and revolved about the shell method because we use cylindrical shells.

cross section

If we add all the cylinders from the smallest to the largest:


Find the volume generated when this shape is revolved about the y axis.

We can’t solve for x, so we can’t use a horizontal slice directly.


If we take a vertical slice the y axis.

and revolve it about the y-axis

we get a cylinder.

Shell method:


Note: the y axis.

When entering this into the calculator, be sure to enter the multiplication symbol before the parenthesis.


When the strip is parallel to the axis of rotation, use the shell method.

When the strip is perpendicular to the axis of rotation, use the washer method.

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