Consider the region bounded by: y=4-x, x=0, y=0

Question

(a.) Find the volume of the solid obtained by revolving about the x-axis.

(b.) Find the volume of the solid obtained by revolving about the y-axis.

(c.) Find the volume of the solid obtained by revolving about the line x=-2

Comments

Since this is basically a cone rotated, can't I just say:
V= 1/3*pi *r^2 *h.
1/3 pi *4^2 *4= my 64pi/3 units^3.

Answer 1

a.) [0,4] Int. pi(4-x)^2 dx= -1/3(4-x)^3 +C 1/3 of 64 64pi/3 units^3 is volume of object rotated around x- axis