Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on the right by the graph of g(y)=4/y and on the left by the y-axis for 2 ≤ y ≤7, about the x-axis.

Answer 1

X=4/y implies y=4/x.

When y =2, x=2, when y =7, x=4/7

( element of volume, dV= 2*pi*yxdy

Dv=2×pi*4*dy

V=8×pi×dy

V=8×pi[y] for y=2 to y=7

=40×pi cubic units

Answer 2

x = 4/y; y = 2 x = 2; y = 7, x = 4/7.

Volume v = 2π∫_4/7²y·4/ydy = 2π·4y_4/7² = 80π/7