A cylindrical rod of height 64 cm is melted to form 12 solid spheres of equal radius. What is the radius of each sphere?

Q.A cylindrical rod of height 64 cm is melted to form 12 solid spheres of equal radius. What is the radius of each sphere? (a) 2 cm (b) 4 cm (c) 8 cm (d) 16 cm

Answer: B

Let the radius of each sphere be \( r \) cm. ∴ According to the question, \[ \frac{4}{\cancel{3}}\pi r^3 \times \cancel{12}4 = \pi r^2 \times 64 \] i.e., \[ 16r = 64 \] So, \[ r = 4 \] ∴ The radius of each sphere is 4 cm.