Volume method, having trouble picturing

In summary, the conversation discusses the concept of using the washer method for finding the volume of a solid of revolution. The speaker is trying to understand if the region enclosed by x=y^2 and x=y+1, when revolved around the y-axis, results in a "hollow" washer shape. They clarify that the bounds of y=-1 and y=2 are not on the axis, meaning that the region between the points of intersection and the y-axis does not contribute to the volume. The speaker also mentions a resource with a similar example and a diagram provided for better understanding.
  • #1
Saladsamurai
3,020
7
So I know it is the "washer" method...but because the book says it is.

The region enclosed by [tex]x=y^2[/tex] and [tex]x=y+1[/tex] revolved around the y-axis.

Now I think I see it , but is it a "hollow" washer because my bounds y=-1 and y=2 (where the curves intersect) are not ON the axis, thus my coss sections are not disks...

that is to say "the region between the points of intersection and the y-axis does not get "swept out" during the revolution"...

I know this is tricky without a diagram,
thanks,
Casey
 
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FAQ: Volume method, having trouble picturing

What is the volume method and how is it used in science?

The volume method is a technique used in science to measure the amount of space occupied by a substance or object. It involves calculating the volume of a solid, liquid, or gas using various methods such as displacement, graduated cylinders, or mathematical formulas.

What are some common units of measurement for volume?

Some common units of measurement for volume include liters, milliliters, cubic meters, and gallons. The unit used depends on the size and type of substance being measured.

How does the volume method relate to density?

The volume method is used to determine the density of a substance, which is the mass per unit volume. By measuring the volume of a substance and its mass, scientists can calculate its density using the formula D=m/v.

Can the volume method be used for irregularly shaped objects?

Yes, the volume method can be used for irregularly shaped objects. One way to do this is by using the displacement method, where the object is placed in a container of water and the change in water level is measured to determine its volume.

Are there any limitations to using the volume method?

One limitation of the volume method is that it may not be accurate for measuring substances that are highly reactive or unstable. In these cases, other methods may need to be used to determine volume. Additionally, human error and equipment limitations can also affect the accuracy of the measurements.

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