How do you find the volume of the region bounded by #y=sqrt x#, y=0, x=0, and x=4 is revolved about the x-axis?

Question

29717 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-06-30T22:11:36

#= 8 pi#

enter image source here

The volume of the small strip of width dx is given by

#dV = pi y^2 dx# where #y = sqrt x# represents the radius of the revolution at that given value for x

so #dV = pi \ x \ dx#

and

#V = pi int_0^4 \x \ dx#

# = pi[x^2/2]_0^4 = 8 pi#