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## Homework Statement

Find the volume of the solid that lies above the cone

ϕ=pi/3

and below the sphere

ρ=4cosϕ

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## Homework Equations

Find the centroid of the solid in part (a).

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## 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

∫0→pi/3∫0→2pi∫0→4cosϕ (ρ^3cosϕsinϕdρdθdϕ)

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)