The radius of cross - section of a right circular rod is 3.2 dcm . The rod is melted to make 21 solid spheres . If the rdius of each sphere be 8 cm , then what will be the length of the rod ?

Explanation

The radius of the right circular rod is 3.2 dcm .
Let the length of the rod = x cm
` :. ` the volume of the rod `= pi xx (32 )^(2) xx "cc"`
The radius of each spheres = 8 cm
` :. ` the volume of each sphere = ` 4/3 xx pi xx (8)^(3) " cc"`
So , the volume of 21 spheres ` = 21 xx 4/3 xx pi xx (8)^(3) " cc " `
` = 28 xx 512 pi "cc "`
As per question , ` pi xx 32 x 32 xx x = 28 xx 512 pi `
` rArr x = (28 xx 512 )/(32 xx 32 ) = 14 `
Hence the required length of the rod = 14 cm