What is the least number of solid metallic spheres, each of 6 cm diameter, that should be melted and recast to form a solid metal cone whose height is 45 cm and diameter is 12 cm?

Class 10 | Cylinder, Cone and Sphere (Surface Area and Volume) | Exercise 20G | ICSE | Selina

Diameter of solid metallic sphere = 6 cm

So, its radius = 3 cm

Height of solid metal cone = 45

Diameter of metal cone = 12 cm

Its radius = 6 cm

Let the number of solid metallic spheres be ‘n’

$\begin{array}{*{35}{l}} Volume\text{ }of\text{ }1\text{ }sphere\text{ }=\text{ }4/3\text{ }\pi \text{ }{{\left( 3 \right)}^{3}} \\ Volume\text{ }of\text{ }metallic\text{ }cone\text{ }=\text{ }1/3\text{ }\pi {{6}^{2}}~x\text{ }45 \\ \end{array}$

Hence, n = Volume of metal cone/ Volume of 1 sphere

$\begin{array}{*{35}{l}} n\text{ }=\text{ }\left( 1/3\text{ }\pi {{6}^{2}}~x\text{ }45 \right)/\text{ }\left( 4/3\text{ }\pi \text{ }{{\left( 3 \right)}^{3}} \right) \\ =\text{ }\left( 6\text{ x }6\text{ x }45 \right)/\text{ }\left( 4\text{ x }3\text{ x }3\text{ x }3 \right) \\ n\text{ }=\text{ }15 \\ \end{array}$

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