Question

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.

Answer 1

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 = \(\frac{4}{3}π R^3\)

Volume of 3 sphere = \(3\times{\frac{4}{3}}πR^3\) ……. (2) 

From eq 1 and eq 2 

⇒ 3 × (\(\frac{4}3\)) π R³ = 160 × 2

⇒ \(R^3 = \frac{160\times2}{3\times\frac{4}{3}π}\)

⇒ R = 2.94 cm