Question

A solid metallic sphere of diameter 21 cm is melted and recast into a number of smaller cones, each of diameter 7cm and height 3 cm. Find the number of cones so formed

Answer 1

Answer:

$\huge \sf \orange { \star} \sf \pink{ \mathfrak{Solution }}$

Diameter of sphere =21 cm

$\tt \: Radius = \frac{21}{2} cm$

Height of the cone =3cm

$\tt \: Radius \: of \: the \: cone  = \frac{7}{2} cm$

$\tt \: Volume \: of \: the \: sphere  = \frac{4}{3} \pi {r}^{3}$

$\tt \: = \frac{4}{3} \pi \times ( {\frac{21}{2} })^{3} \: {cm}^{3}$

Let n be the number of cone formed,

then,

n = (volume of the sphere)/(volume of cone)

$\tt \: n = \frac{( \frac{4}{3} \times \pi \times ({ \frac{21}{2} })^{3} }{ \frac{1}{3} \times \pi \times ({ \frac{7}{2} })^{2} \times 3 }$

$\tt \green{∴ \: n \: = \: 378}$

Number of cones formed = 378

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