The radius of a sphericla ball of iron is 1.5 cm .It is melted and recast into three sperical balls .If the radii of two such balls are 0.75 cm and 1 cm , then find the radius of 3rd bal .

Explanation

Radius of given ball r = 1.5 cm
Radius of first ball `r_(1)=0.75 cm`
Radius of second ball `r_(2)=1cm`
Let the radius of third ball =`r_(3)`
Now,
Volume of first ball+ Volume of second ball + Volume of third ball =volume of given ball
`(4)/(3)pir_(1)^(3)+(4)/(3)pir_(2)^(3)+(4)/(3)pi_(3)/(3)=(4)./(3)pir^(3)`
`r_(1)^(2)+r_(2)^(3)+r_(3)^(3)=r^(3)`
`r_(3)^(3)=r^(3)-r_(1)^(3)-r_(1)^(3)=(1.5)^(3)-(0.75)^(3)-(1)^(3)`
`=((3)/(2))^(3)-((3)/(4))^(4)-(1)^(3)=(27)/(8)-(27)/(64)-(27)/(64)-1=(216-27-64)/(64)`
`r=(216-91)/(64)=(125)/(64)=((5)/(4))^(3)=(1.25)^(3)`
`r^(3)`=1.25cm
Radius of third ball =1.25 cm
Radius of third ball = 1.25