A torus is formed by revolving the region bounded by the circle x² + y² = 1 about the line x = 2 (see figure below). -1 - 1 y Volume = cubic units. 1 2 X Find the volume of this "doughnut-shaped" solid. (Hint: The integral √1 - 2² da represents the area of a semicircle. So you can find this specific integral without using antiderivative.)

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
A torus is formed by revolving the region bounded by the circle x² + y² = 1 about the line * = 2 (see figure
below).
-1
-1
y
1
2
I
X
Find the volume of this "doughnut-shaped" solid.
(Hint: The integral √1 - 2² da represents the area of a semicircle. So you can find this specific integral
without using antiderivative.)
Volume = cubic units.
Transcribed Image Text:A torus is formed by revolving the region bounded by the circle x² + y² = 1 about the line * = 2 (see figure below). -1 -1 y 1 2 I X Find the volume of this "doughnut-shaped" solid. (Hint: The integral √1 - 2² da represents the area of a semicircle. So you can find this specific integral without using antiderivative.) Volume = cubic units.
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