A cube of a glass of 5 cm side and mass 306 g, has a cavity inside it. If the density of glass is 2.55 gcm⁻³. Find the volume of the cavity. Ans. (5 cm³)


Given:  

Length of a side of Glass Cube = L = 5 cm = 0.05 m
Volume of the cube with out cavity = V= L³ = (0.05 m)³ = 0.000125 m³ =1.25ｘ1o⁻⁴ m³

Mass of a Gold bar = m = 306 g = 0.306 kg
Density of a Glass = 𝜌 = 2.55 gcm⁻³ =  2.55 ｘ1o³ kg m⁻³

To Find:

Volume of the cavity = ?

Solution:   

As given the Volume of the cube without cavity = V = 1.25ｘ1o⁻⁴ m³ and to find the Volume of the cube with a cavity we have the formula as


Volume of the cube with cavity  = `\frac {Mass}{Density}`

 by putting values

Volume of the cube with cavity = `\frac {0.306 kg}{2.55 ｘ1o³ kg m⁻³}`

Volume of the cube with cavity = 0.12 ｘ10⁻³ m³

or

Volume of the cube with cavity = 1.20 ｘ10⁻⁴ m³

Now Volume of the cavity can be found easily by just taking the difference of the Volume of the cube without a cavity and with a cavity

The volume of the cavity =Volume of the cube without cavity - Volume of the cube with cavity 

Volume of the cavity = 1.25ｘ1o⁻⁴ m³ - 1.20 ｘ10⁻⁴ m³

Volume of the cavity = 0.05ｘ1o⁻⁴ m³ 

Volume of the cavity = 5ｘ1o⁻⁶ m³ 

Or

Volume of the cavity = 5 cm³  ( 1 cm³ = 1o⁻⁶ m³)

Thus, the volume of the cavity is  5 cm³

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