Question

16 A solid spherical ball of iron with radius 6 cm is melted and recast into three
sold spherical balls. The radi of the two balls are 3 cm and 4 cm respectively.
determine the diameter of the third ball​

Answer 1

vol. of solid sphere = 4/3πr^3

according to the question

vol of big sphere is equal to the sum of three small sphere

R = 6cm

r1 = 3cm

r2 = 4cm

r3 = x cm

4/3πR^3 = 4/3πr1^3 + 4/3πr2^3 + 4/3πr3^3

4/3πR^3 = 4/3π(3^3 +4^3 + x^3)

6^3 = 27+64+x^3 (4/3π will get cancelled )

216 = 91 + x^3

216 - 91 = x^3

x^3 = 125

x^3 = 5 ^3

x = 5 cm

the diameter of the third ball is 10cm

hope it will help you