A solid metallic sphere of radius x cm is melted and then drawn into 126 cones each of radius 3.5 cm and height 3 cm. There is no wastage of material in this process. What is the value of x?

10.5

We know that,

The volume of sphere = \(\frac{4}{3}\)πR³

Volume of cone = \(\frac{1}{3}\)πr²h

We have,

Total number of cones = 126

Radius and Height of cone = 3.5 cm and 3 cm respectively.

According to the question

\(\frac{4}{3}\)πx³ = 126 × \(\frac{1}{3}\) × πr²h

= x³ = \(\frac{126}{4}\) × 3.5 × 3.5 × 3

= x³ = 3 × 3 × 3.5 × 3.5 × 3.5 × 3 = 10.5 cm