Question

A hollow metallic sphere is 2 cm thick all around and has an external diameter of 12 cm. Find the radius of the solid sphere made by recasting this hollow sphere.

Answer 1

External diameter of hollow sphere = 12 cm 

External radius = R = 6 cm 

Internal diameter of hollow sphere =  ( 12 - 4) cm= 8 cm 

Internal radius = r = 4 cm 

Volume of metal used = `4/3pi(R^3 - r^3)`

= `4/3 xx 22/7 xx (6^3 - 4^3)`

= `4/3 xx 22/7 xx 152`

= 636.95 `"cm"^3`

Volume of metal used = 636.95 cm³ = volume of sdid sphere 

⇒ `4/3pir^3 = 636.95`

⇒ `4/3 xx 22/7 xx r^3 = 636.95`

⇒ `r^3 = (636.95 xx 3 xx 7)/(4 xx 22)`

⇒ `r^3 = 151.99 = 152`

⇒ r = 5.34 cm

Radius of the solid sphere = 5.34 cm