Question

A solid metallic sphere of radius 14 cm is melted and recast into a number of smaller cones, each of radius 7 cm and height 4 cm. The number of cones so formed is

• A. 64
• B. 108
• C. 56
• D. 98

Answer 1

The correct option is C 56

Let radius of metallic sphere be R, and radius and height of the smaller cones be r and h respectively.

∴R = 14 cm, r = 7 cm, h = 4 cm

Let n be the number of smaller cones formed.

∴Volume of sphere = n × Volume of 1 cone

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

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

$\Rightarrow 4\times (14{)}^3=n\times (7{)}^2\times 4$

$\Rightarrow n=\frac{4\times 14\times 14\times 14}{7\times 7\times 4}$

$\Rightarrow n=2\times 2\times 14=56$

Hence, the correct answer is option (c).