Question

27 solid iron spheres, each of radius 'xcm'ate melted to form a sphere with radius 'ycm',find the ratio x:y​

Answer 1

Answer:3:1

Explanation:

Given

There are 27 solid spheres of radius x cm

The volume of a sphere is
`(4)/(3)\pi r^3`

The volume of 27 old spheres is the same as the volume of a new sphere

The volume of the old spheres is

`V_o=(4)/(3)\pi x^3`

The volume of a new sphere is

`V_n=(4)/(3)\pi y^3`

Now,
`V_o=V_n`

`\Rightarrow 27* (4)/(3)\pi x^3=(4)/(3)\pi y^3\\\\\Rightarrow ((x)/(y))^3=27\\\\\Rightarrow (x)/(y)=3`