A cylindrical vessel with internal diameter 10 cm and height 10.5 cm is full of water. A solid cone of base diameter 7 cm and height 6 cm is completely immersed in water. Find the volume (i) displaced out of the cylinder (ii) left in the cylinder.
Given internal diameter of cylinder = D = 10 cm
Internal radius of cylinder = R = D/2 = 10/2
Internal radius of cylinder = R = 5 cm
Height of cylinder = H = 10.5 cm
Diameter of solid cone = d = 7 cm
Radius of solid cone = r = d/2 = 7/2
Radius of solid cone = r = 3.5 cm
Height of cone = h = 6 cm
(i)Volume displaced out of cylinder
By Archimedes principle we can easily say that,
Volume displaced out of cylinder = Volume of the solid cone
⇒ V = 22 × 1.75 × 2
∴ V = 77 cm3
The volume displaced out of cylinder is 77 cm3.
(ii)Volume left in cylinder
Volume left in cylinder = Volume of cylinder – Volume displaced out
Volume of cylinder = π(R)2H
⇒ Volume of cylinder = π × (5)2 × 10.5 (putting the given values)
⇒ Volume of cylinder = π × 25 × 10.5
⇒ Volume of cylinder = π × 262.5
⇒ Volume of cylinder = 22 × 37.5
∴ Volume of cylinder = 825 cm3→eqn1
Volume left in cylinder = 825 – 77 (from eqn1 and (i))
∴ Volume left in cylinder = 748 cm3
The volume left in the cylinder is 748 cm3.