Question

A solid metal cone with base radius 18 cm and height 10 cm, is melted to form solid spherical balls each of diameters 6 cm. The number of such balls made is

• A. 20
• B. 25
• C. 30
• D. 40

Answer 1

The correct option is C 30

Let n be the number of spherical balls formed by melting the solid cone.

Let r and h be the radius and height of cone.

$\therefore r=18cm,h=10cm$

Radius of spherical balls, $R=\frac{6}{2}=3cm$

∴ Volume of solid cone = n × volume of 1 spherical ball

$\Rightarrow \frac{1}{3}\pi r^{2}h=n\times \frac{4}{3}\pi R^3$

$\Rightarrow 18\times 18\times 10=n\times 4\times (3{)}^3$

$\Rightarrow n=\frac{18\times 18\times 10}{4\times 27}=30$

Hence, the correct answer is option (c).