A solid metallic spherical ball of diameter 6 cm is melted and recast into a cone with diameter of the base as 12 cm. The height of the cone is (a) 2 cm       (b) 3 cm       (c) 4 cm        (d) 6 cm

Explanation

Volume ball `V_{s}=frac{4}{3} pi r^{3}`

`

=frac{4}{3} 3^{3} pi=36 pi cm^{3}`


cone volume made from sphere `V_{c}=frac{1}{3} pi r^{2} h`

`

=frac{1}{3} 6^{2} times h pi=12 h pi cm^{3} `

`
Rightarrow V_{s}=V_{c} `

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Rightarrow 36 pi=12 h pi`

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