Question

A sphere of lead of diameter 6 cm is melted and recast into three spherical balls. The

diameters of these are 3 cm and 4 cm respectively. Then, the diameter of third one is

(a) 8 cm
(b) 10 cm
(c) 5 cm
(d) 15 cm​

Answer 1

Answer:

5 cm

Step-by-step explanation:

Volume of sphere=(4/3)πr³

In given lead sphere,

radius =6/2=3cm

volume =(4/3)π3³cm³

for small spherical balls

volume of 1st ball =(4/3)π(3/2)³

volume of 2nd ball =(4/3)π2³

let radius of 3rd sphere be r

then it's volume =$4/3)πr³

Now according to question,

(4/3)π3³=(4/3)π27/8. +(4/3)π8 +(4/3)πr³

(4/3)π27=(4/3)π (27/8 + 8 + r³)

27=27/8 +8 +r³

19=27/8 + r³

(152-8)/8=r³

18=r³

r ~ 2.2

diameter =5cm approximately