Question

Find the volume of the portion of the solid sphere rholess than or equals5 that lies between the cones variant phiequalsStartFraction pi Over 6 EndFraction and variant phiequalsStartFraction 5 pi Over 6 EndFraction .

Answer 1

Volume = (250π√3)/3 unit³

Explanation:

The shape is a solid sphere

Where rho = ρ

ρ ≤ 5

Where Phi = φ

φ = π/6 (lower limit)

φ = 5π/6 (upper limit)

Note 1π rad = 180°

We would apply triple integrals and spherical coordinates to solve for the volume of a solid sphere.

See attachment for details

From calculations,

The volume of the portion of solid sphere = Volume = (250π√3)/3 unit³