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A homogeneous circular disc with radius R = 5.05 m and thickness t = 10.1 · 10^−3 m rotates around the z-axis (perpendicular to the disc, see figure). A rectangular hole is cut out in the centre of the disc with the base b = 4.642 m and the height h = 4.72 m. Calculate the mass of the disc if there is no hole and the density of the disc varies according to ρ(r) = 1.39 · r kg/m^3, where r is the distance to the center of the disc. Tip: use m = 2πt∫r · ρ(r) dr.
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