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?
Answer & explanation
Correct answer: option 4
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