Given: Diameter of sphere = 16 cm Height of cylindrical vessel = 32 cm Diameter of cylindrical vessel = 16 cm Concept Used: When a solid body is completely immersed in water then, The volume of the water displaced = volume of the solid body Formula Used: (i) Volume of a Sphere = (4/3)πR3 where, R = Radius of the sphere Also, R = D/2 (ii) Volume of a Cylinder = πr2h where, r = Radius of the cylinder, & h = Height of the cylinder Calculation: [ alt="vesseessl" src="//storage.googleapis.com/tb-img/production/21/04/vesseessl.png" style="width: 700px; height: 310px;"> Let volume of the Metallic sphere be 'v' and volume of the water in cylindrical vessel before immersing the metallic sphere be 'V'. According to the question, v = (4/3)πR3 ⇒ (4/3) × π × (8)3 ⇒ (4/3) × π × 512 ⇒ (2048/3)π cm3 Let the volume of the water in the cylindrical vessel before immersing the metallic sphere be 'V'. Now, V = Volume of the cylindrical vessel ⇒ πr2h ⇒ π × (8)2 × 32 ⇒ π × 64 × 32 ⇒ 2048π cm3 So, Volume of water remaining in cylindrical vessel = V - v ⇒ 2048π - (2048/3)π ⇒ {2048 - (2048/3)}π ⇒ {(3 × 2048 - 2048)/3}π ⇒ {(2 × 2048)/3}π ⇒ (4096/3)π cm3 ∴ The volume of the water remaining in the vessel after taking out the metallic sphere is (4096/3)π cm3