A solid metallic sphere of radius 6.3 cm is melted and recast into a right circular cone of height 25.2 cm. What is the ratio of the diameter of the base to the height of the cone?

1 : 2

We know that,

Volume of sphere = $\frac{4}{3}$πR³ 

Volume of cone = $\frac{1}{3}$πr²h

We have,

Radius of the sphere = 6.3 cm

Height of the cone = 25.2 cm

According to the question,

$\frac{4}{3}$πR³ = $\frac{1}{3}$πr²h

$\frac{4}{3}$× 6.3 × 6.3 × 6.3 = $\frac{1}{3}$ × r² × 25.2

on solving further,

r = 6.3

Diameter = 2 × 6.3 = 12.6

Required ratio = 12.6 : 25.2 = 1 : 2