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

The Radius of each sphere is 2.94 cm

Step-by-step explanation:

Given as :

A vessel in the shape of a cuboid contains some water.

The Area of base of cuboid vessel = A = 160 cm²

The height of cuboid vessel = H = 12 cm

Three identical spheres are immersed in the water, the level of water is increased by 2 cm

So, Height of water level in vessel = h = 2 cm

Let  The radius of sphere = r cm

According to question

Volume of cuboid = Area of base × height

Or,  V = A × h

Or, V  =  160 cm² × 2 cm

∴    V = 320 cm³

So, volume of cuboid = 320 cm³          ...1

Again

Volume of Sphere = v = $\dfrac{4}{3}$ × π × radius³

Or,  v =  $\dfrac{4}{3}$ × 3.14 × r³

So, volume of 3 sphere = 3 v

i.e volume of three sphere = 3 × $\dfrac{4}{3}$ × 3.14 × r³            .....2

As sphere immersed in vessel

From eq 1 and eq 2

So, Volume of vessel = volume of sphere

i.e   320 cm³  =  3 × $\dfrac{4}{3}$ × 3.14 × r³  

Or, 320 = 4 × 3.14 × r³  

or, 320 = 12.56  × r³

Or,   r³ = $\dfrac{320}{12.56}$

i.e   r³ = 25.477

∴    r = ∛25.477

i.e  r = 2.94 cm

So, The Radius of each sphere = r = 2.94 cm

Hence,  The Radius of each sphere is 2.94 cm Answer