A vessel is in the form of a hemi-spherical bowl mounted by a hollow cylinder. The diameter of the sphere is 14 cm and the total height of the vessel is 13 cm. Find the capacity. (π = 22/7)
                                                                
Diameter of the sphere = d = 14 cm ⇒ Radius of the sphere = r = 7 cm
Total height of the vessel = 13 cm ⇒ Height of the cylinder = h = 13 – 7 = 6 cm ∴ Volume of the hemispherical part = π r3
                                                          = × × 7 × 7 × 7
                                              = 718.67 cu. cm ∴ Volume of the cylindrical part = π r2h
                                         = × 7 × 7 × 6
                                         = 924 cu. cm ∴ Capacity of the vessel = (718.67 + 924) cu. cm
                                   = 1642.67cu. cm
14