A vessel in the shape of a cuboid contains some water. If three identical spheres are immersed in the water, the level of water is increased by 2 cm. If the area of the base of the cuboid is 160 cm2 and its height 12 cm, determine the radius of any of the spheres.
Given that area of cuboid =160 cm2
Level of water is increased = 2 cm
Volume of vessel =160× 2 cm3 ……. (1)
Volume of each sphere 3
Volume of 3 sphere 3 ……. (2)
From eq 1 and eq 2
⇒ 3×(4/3) π R3 = 160× 2
⇒ R = 2.94 cm