Question

A solid is formed by rotating the region bounded by the curve y = e^-3x/2 and the x axis between x=0 and x=1 around the xaxis. The volume of this solid is pi/3 * (1 - e^-3). Assuming the solid has constant density delta, find x and y.
x=
y =

Answer 1

Answer:

x = .28

y = 0

Step-by-step explanation:

Voume of disk = pi *r^2 = pi * e^-3x deltax

x = integal 0 to 1 of x * delta*pi*e^-3x deltax / mass = (delta*pi) integal 0 to 1 of x * e^-3x deltax/mass = (delta*pi)0.08898/mass

mass = sigma *(volume)=delta(pi/3*(1-e^-3)) =delta(.995)

x = (delta*pi)0.08898/delta(.995) = .28

by symmetry y=0