IGNOU BMTC 102 2026 - Find the mass of the solid bounded by and , the

Question

Find the mass of the solid bounded by $z = 1$ and $z = x^2 + y^2$ , the density function being $\delta(x, y, z) = |x|$ .

09 Jan 2026

Answer :

Word Count : 245

The solid is bounded below by (z = x^2 + y^2) and above by (z = 1), with density (\delta(x,y,z) = |x|). To find the mass, we integrate the density over the volume: [ M = \iiint_V \delta(x,y,z) , dV = \iiint_V |x| , dV ] The projection of the solid on the (xy)-plane is where (x^2 + y^2 \le 1), i.e., the unit disk. Using cylindrical coordinates: [ x = r\cos\theta, \quad y

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