# Thread: a surface area multiple integral question..

1. ## a surface area multiple integral question..

hello.. i do not understand this question was hoping that someone could guide me through this..

A flat circular disc, of radius R, can be modelled as a thin disc of negligible thickness.
It has a surface mass density function given by f(r,0) = k(1-r^2/R^2),
where k is the surface density at the centre and r is the distance from the centre of the disc.

Using area integral in plane polar coordinates, calculate the total mass of the disc, in kg, when R = 0.15m and k = 12 kg/m^2

2. ## Re: a surface area multiple integral question..

Should that be f(r, θ) = k(1-(r^2/R^2))?

The differential for an element of area is given by dA = r dr dθ , if you're using an iterated integral.

If you don't understand iterated integrals, then use dA = 2π r dr .

The mass is given by: $m=2\pi \int_0^R\ f(r,\theta)\,r\,dr\,.$