A sphere, centered at the origin, has radius 4. Find integrals that compute its volume, using Cartesian, cylindrical, and spherical coordinates. For your answers heta = theta, phi = phi, and ho = rho. Cartesian int_a^b int_c^d int_e^f p(x, y, z) dz dx dy = int_0^4 int_0^{sqrt(16-y^2)} int_0^{sqrt(16-x^2-y^2)} 1 dz dx dy Cylindrical int_a^b int_c^d int_e^f f(r, heta, z) dz dr d heta = int_0^{2pi} int_0^4 int_{-sqrt(16-r^2)}^{sqrt(16-r^2)} r dz dr d heta Spherical int_a^b int_c^d int_e^f g( ho, heta, phi) d ho d heta dphi = int_0^{pi} int_0^{2pi} int_0^4 sigma^2sin(fi) d ho d heta dphi
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