Question

Use the Shell Method to find the volume of a solid obtained by rotating the region

about the -axis
Assume =3
and =2.

Answer 1

V = 38π/3 cubic units

Explanation:

The formula for the shell method is given by:

V = 2π ∫(y)(x)dx

where x and y are the equations of the upper and lower bounds of the region being rotated. In this case, we have:

y = x

x = 2

So, the volume is given by:

V = 2π ∫(x)(x)dx from x=2 to x=3

V = 2π (x^3/3) from x=2 to x=3

V = 2π ((3^3/3) - (2^3/3))

V = 2π (27/3 - 8/3)

V = 2π (19/3)

V = 38π/3 cubic units