Find the volume of the solid that lies above the cone
and below the sphere
Find the centroid of the solid in part (a).
The Attempt at a Solution
For the volume I got 10pi which I am fairly sure is correct. I attempted trying to calculate the centroid and i got a different answer from the book. I have (0,0,21/40)
and I would like to know what did i do incorrect. I calculated ybar and xbar and i got 0.
for zbar, i did the following
the book's answer for the inner integration of rho was ∫0→2pi∫0→pi/3 (cosϕsinϕ(64cos^4(ϕ))dϕdθ
is this correct? isn't supposed to be ∫0→2pi∫0→pi/3 (cosϕsinϕ(64cos^4(ϕ)/4)dϕdθ?
or am I wrong? (I divided by 4, because that's the rule of integration)