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In the above figure, each slice has the shape of a washer so its area equals the area of the entire circle minus the area of the hole.

(a) A thin rectangle for approximating the area under a curve. (b) A representative disk formed by revolving the rectangle about the x-axis.

The first region is simple, it can be done by the washer method. The top part is f(x) which is sin(x) and the bottom part is g(x) which is ...

One of the most difficult things to do when working with volumes of solids of revolution is to visualize the shape that is being formed.

Notice that one thing we can easily find is the area of a single horizontal slice of the ball. This is the shaded disk at the top of the diagram, ...

Probably because none of the textbooks or online sources didn't just come out and say what to do in plain English:

(a) A thin rectangle in the region between two curves. (b) A representative disk formed by revolving the rectangle about the x-axis.

So what we did was plug in our outer function and inner function where they belong and integrated it from the starting point to the ending point.

Using the above technique, we know the volume of a cylinder to be: V = h R 2 π , where h is the height of the cylinder. Now consider another shape, ...

... high and its shape can be approximated by the graph of this equation revolved about the y-axis: The volume can be calculated using the disk method with ...

(a) The function f(x)=x over the interval [1,4]. (b) The solid of revolution obtained by revolving the region under the graph of f(x) about the x-axis.

(We looked at this method last lesson). The shape of the slice is a disk, so we use the formula for the area of a circle to find the volume of ...

Do not get confused looking at the incremental values represented using the Greek sign of delta (δ). Since this three dimensional figure is made up of many ...

pedrojperez/iStock/GettyImages. Measuring the volume of an irregularly shaped object using geometry ...

Boker's is a leading stamping manufacturer of C washers. C-washers obtain their name for being in the shape of a "C" as they have a slot cut from the center ...

First question is about finding the volume of a shape with respect to y=√32 I don't know which method to use shell or washer?