Question

A cylindrical rod of rod iron whose height is eight times its radius is melted and cast into spherical balls each of half the radius of the cylinder. the number of spherical balls is:

• A. $12$
• B. $16$
• C. $24$
• D. $48$

Answer 1

Answer: (D)

$48$

Let radius of iron rod = r
∴∴ Height = 8r
∴∴ Volume of iron rod
=π×(r)2×8r⇒8πr3=π×(r)2×8r⇒8πr3
⇒⇒ Radius of spherical ball =r2=r2
Volume of spherical ball
=43π(r2)3=43π(r2)3
Let n balls are casted
∴n×43π(r38)=8πr3∴n×43π(r38)=8πr3
⇒n6=8⇒n=48