Question

A sphere of radius 4 cm is carved from a homogeneous sphere of radius 8 cm and mass 160 g. the mass of the smaller sphere is

Answer 1

The ratio of the volume of the smaller sphere to the larger =  (4)^3 / (8)^3  = 1/8

 

Assuming a uniform density:    D = M/V .......so......

 

160 / 8  = Mass of the smaller sphere / 1

 

Mass  of the smaller sphere  = 20 g

Answer 2

The mass of smaller sphere is 20g

Radius of the sphere = 4cm (Given)

Homogeneous radius of the sphere = 8cm  (Given)

Mass of the sphere = 160g  (Given)

Calculating the ratio of the volume of the smaller sphere to the larger sphere -

=  4³ / 8³

= 64/ 512

= 1/8

Let there be a uniform density of the sphere -

D = M/V, where

D = Mass of the smaller sphere / 1  

Thus,

= 160 / 8  

= 20

Therefore, mass of the smaller sphere is  = 20g