Answer :

base radius of cone= r_{c} = 3 cm

Height of cone = h = 6 cm

Radius of sphere = r_{s} = 9 cm

volume of cone = πr_{c}^{2}h

Volume of sphere = πr_{s}^{3}

Let n be the number of cones made

As the sphere is melted and then the cones are made from the same amount of melted sphere therefore the volume remains same

i.e. volume of n cones made = volume of sphere

⇒ n × πr_{c}^{2}h = πr_{s}^{3}

⇒ nr_{c}^{2}h = 4r_{s}^{3}

Substituting values

⇒ n × 3^{2} × 6 = 4 × 9^{3}

⇒ n × 6 = 4 × 9 × 9

⇒ n = 6 × 9

⇒ n = 54

Number of cones formed = 54

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