Question

An irregularly shaped chunk of concrete has a hollow spherical cavity inside. The mass of the chunk is 83.4 kg, and the volume enclosed by the outside surface of the chunk is 0.198 m³. What is the radius of the spherical cavity?

Answer 1

Solution:-

Given –

             Mass of the chunk = 83.4 kg

            Volume of the chunk = 0.198 m^3

To solve this you need to know the density of concrete without the hole the range of values mostly from 2400 kg/m^3

Since density is mass / volume, we can find the the mass of a whole chunk of concrete of volume 0.198 m^3

P = m/v   : m = pv

= 2400 kg/m^3 * 0.198m^3

m = 475.2 kg

However, the mass given for the chunk with the spherical void is given as 83.4 kg so that missing mass of the void is,

m (void) = 475.2kg – 83.4kg

m (void) = 391.8 kg

The volume of the void then is,

V = m/p

= 391.8 kg / 2400 kg/m^3

V = 0.16 m^3

The radius of the void is found from the formula for the volume of a sphere,

V = 4πr^3 / 3

r = (3v / 4π) ^ 1/3

= [3(0.16)/4*3.14] ^ 1/3

r = 0.34 m

The radius of the spherical cavity is r = 0.34 m