Washer Method
In Washer Method we take the axis of revolution is not the boundary of the plane region and the cross section are taken perpendicular to the axis of revolution. Washer are considered to be the disk with hole. Now to calculate the area of the washer the formula is, π(R2 – r2) and its volume is the area times its thickness.
Now volume of the solid generated by revolving the region bounded by y = f(x) and y = g(x) in the interval [a, b] if f(x) ≥ g(x) then its volume about x-axis is,
V = [Tex]\int_b^a [/Tex] π{|f(x)|2 – |g(x)|2} dx
If the region is bounded by x = f(y) and x = g(y) in the interval [a, b] if f(y) ≥ g(y) then its volume about y-axis is,
V = [Tex]\int_b^a [/Tex] π{|f(y)|2 – |g(y)|2} dy
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Volume of Solid of Revolution
Volume of Solid of Revolution: A solid of revolution is a three-dimensional shape created by spinning a two-dimensional curve around a line within the same plane. The volume of such a solid can be computed using integration. The most typical techniques for determining the volume include the disc method, the shell method, and Washer Method.
Volume of Solid of Revolution is generated by revolving a plane area R about a line L known as the axis of revolution in the plane. We use the concept of definite integrals to find the volume of the curve that revolves around any line.
Here in this article, we will learn about the Volume of Solids of Revolution, Disk Method, Washer Method, Volume of Solid of Revolution Examples, and others in detail.
Table of Content
- Volume of Solid of Revolution
- Parametric Form
- Polar form
- Volume of Revolution Formula
- Methods of Volumes of Solids of Revolution
- Disk Method
- Washer Method
- Volume of Solid of Revolution Examples
- Volume of Solid of Revolution Problems