Question

A large new sphere is made by melting two metal sphere of radii `r_(1) "unit and" r_(2)` unit respectively. Find the radius of the large sphere.

Answer 1

The total volume of the sphere `=(4)/(3)pi(r_(1)^(3)+r_(2)^(3))` cubic,unit.
Now, let the radius of the large be r unit,
`therefore` the volume of the large sphere `=(4)/(3)pir^(3)` cu,unit.
As per condition `(4)/(3)pir^(3)=(4)/(3)pi(r_(1)^(3)+r_(2)^(3)) rArr r=root(3)(r_1^3+r_2^3).`
Hence the required of the large sphere `=root(3)(r_1^3+r_2^3).` unit.