Mass of gold in a hemispherical ore with density kz

[kd001]

Homework Statement

A hemispherical piece of ore of radius a contains flakes of gold. The flat base
of the ore is in the x, y plane and its curved surface is in the region z > 0,
where x, y, z are cartesian co-ordinates with origin at the centre of the base.
The gold density is kz kg m−3, where k is a constant. What is the total mass
of gold in the ore?

Homework Equations

The Attempt at a Solution

Using multiple integrals I got an answer of (pika⁴)/4 kg.

Can someone please check if this is the correct answer.

Thanks a lot. A simple yes or no will do.

 

[gabbagabbahey]

Looks good to me!

 

[kd001]

Thanks!