Two solid sphere of radii 3 cm and 4 cm are melted to make a hollow sphere of external radius of 6 cm, then wahat will be the thickness of the new hollow sphere?

Explanation

The radii of the twoo solid spheres are 3cm and 4 cm.
So, the total volume of the two spheres
`=((4)/(3)pixx3^(3)+(4)/(3)pixx4^(3)) "cc" =(4)/(3)pi(27+64) "cc"=(4)/(3)pixx91` cc.
The external radius of the hollow sphere =6 cm
Let the internal radius of it =r cm.
`:.` the volume of material of the hollow sphere` =(4)/(3)pi(6^(3)-r^(3)) "cc" (4)/(3)pi(216-r^(3))` cc
`:. (4)/(3)pi(216-r^(3))=(4)/(3)pixx91 "or," 216-r^(3)=91 "or", =r^(3)=125 "or" r^(3)=5^(3)rArrr=5`.
`:.` thickness of the hollow sphere =(6-5)cm =1cm
Hence the thickness of the hollow sphere =1 cm .