) Consider the circle of radius 2 centered on the x-axis at the point (5, 0). If you rotate this circle around the y-axis, you get a torus (a. k.a a doughnut). Find the surface area of the torus using an integral.

236.87 Square Units

Step-By-Step Explanation

Consider a torus generated by the rotation of the circle about the y-axis  given below.

The perimeter of its cross section is 2\pi r. When it involves the y-axis:

Its total surface area:

For a circle radius 2 centered on the x-axis at the point (5, 0).

r=2. x=5, y=0

5-R=2

R=5-2=3

Therefore, the total Surface Area is:

3: 2

step-by-step explanation:

shorter piece is 2: 3, so just reverse it, and you get 3: 2

3/4 ÷ 3/4

step-by-step explanation:

basically divide any proper fraction with itself to fit the criteria.

so if we are using 3/4, then:

3/4 ÷ 3/4 = 1

so 1 is the quotient.

and the numerators for both these fractions is 3.   and if we divide the numerators:

3 ÷ 3 = 1

we see that quotient is equal to our original quotient as well.