17.3 Volume of a Torus: the Washer Method - MIT Mathematics
网页By rotating the circle around the y-axis, we generate a solid of revolution called a torus whose volume can be calculated using the washer method. Washer method. We revolve around the y-axis a thin horizontal strip of height dy and width R - r. This generates a disk with a hole in it (a washer) whose volume is dV.
How to integrate the volume of a solid torus (donut-shaped solid)?
网页1. hint: in addition to what Raskolnikov said, it may be simpler to consider the washer method instead of the shell method for setting up your integral. (That is, integrate in y y and consider the area of annuli of the constant y y slices.)
网页Washer Method Problem: By integrating with respect to the variable y, nd the volume of the solid of revolution formed by rotating the region bounded by y= 0, x= 4 and y= p xabout the line x= 6. Solution: This problem was solved in recitation using the shell method. Here we use the washer method. First we sketch the region; see Figure 1. x =4 x =6
6.3.3 The Washer Method - Wolfram Cloud
网页The washer method is really two applications of the disk method. We compute the volume of the entire solid without the hole (by the disk method) and then subtract the volume of the hole (also computed by the disk method).
How to find the Volume of a Torus? - GeeksforGeeks
网页2022年4月26日 · Using Washer method, the volume of the given solid torus can be written as, V = = (4πR) (1/2) (πr 2) = 2π 2 r 2 R. This derives the formula for volume of a torus. Sample Problems. Problem 1. Find the volume of the torus with an inner radius of 7 cm and an outer radius of 14 cm. Solution: We have, r = 7 and R = 14.
网页Washer method: slice along the rotating direction Q. Need to solve cubic equation for Hard, or impossible in other situations like Abandon. Shell method: slice away from rotating axis. Sec6.3 Volume by cylindrical shell s6.3 Page 1
Volume of the torus with an integral - Mathematics Stack Exchange
网页Find the volume of the torus obtained by rotating the circle $(x-a)^2+y^2=b^2$, where $a>b$, around the y-axis.
ELI5: Volume of a Torus Using Disk/Washer Method
网页2017年8月30日 · The washer method is slicing the bagel into concentric rings which you can then add up to get the volume of the torus. true.
Washer Method -- from Wolfram MathWorld
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Volume of a torus, in terms of big radius R and little radius r, …
网页2012年11月3日 · The volume of a torus can be calculated using the formula V = π^2Rr^2, where R is the big radius and r is the little radius. This formula is derived using the washer method, which involves taking the integral of the cross-sectional area of the torus.
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