/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 56 A torus is formed by revolving t... [FREE SOLUTION] | 91影视

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Chapter 7: Problem 56

A torus is formed by revolving the graph of \((x-1)^{2}+y^{2}=1\) about the \(y\) -axis. Find the surface area of the torus.

Short Answer

Expert verified
The surface area of the torus is \(2\pi^2\) square units.

Step by step solution

01

Identify the values of R and r

For the given equation, the circle that generates the torus has center at (1,0) and radius 1. Thus the larger radius \(R\) is the x-coordinate of the circle center, which is one and the smaller radius \(r\) is the radius of the circle, which is also one.
02

Substitute the values into the formula

Now substitute the identified values \(R=1\) and \(r=1\) into the formula for the surface area of a torus \(A=2\pi^2 Rr\). Giving, \(A=2\pi^2 (1)(1)\).
03

Simplify the expression

Simplifying the expression gives \(A=2\pi^2\).

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