A right, circular cone is made of solid aluminum, with uniform density p=2.70x10

Question

A right, circular cone is made of solid aluminum, with uniform density p=2.70x10^3 k/m^3. Its base, of radius b=12cm sits on the xy plane, and its axis of symmetry lies along the z-axis. The height, measured from the center of the base to the apex, is h=72cm. a) Calculate the mass M of the cone. b) By symmetry, the center of mass of the cone should tie on its axis of symmetry (the z axis in this case). Calculate he z-coordinate of its center of mass (remember its base is centered at the origin).

Explanation / Answer

volume of the cone = 1/3 * pi * r2 * h = 1/3 * 3.14 *122*72 = 10857.34 cm3 = 0.010857 m3

Mass = density*Volume = 2.70*103*0.010857 = 29.314 kg (ans)

SInce it is a symmetric solid,

So Z coordinate will be 1/4 h = 18 cm . from the base(ans)

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