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# 6.3 Shell Method - PowerPoint PPT Presentation

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

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

outer

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:

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 perpendicular to the axis of rotation, use the washer method.

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