Two right circular cones having same base radius of $2.1$ cm but heights $4.1$ cm and $4.3$ cm are melted and recast into a single sphere Find the radius of the sphere so formed

2.1

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2

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4.2

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3.1

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Solution

The correct option is A $2.1$ cm
Volume of the sphere
$\frac{4}{3} π R^{3}$ =volumes of the cones of hights $h_{1}$ and $h_{2}$ with same radius r
$= \frac{1}{3} π r^{2} (h_{1} + h_{2})$
$= \frac{1}{3} \times π \times {(2.1)}^{2} \times (8.4)$
$R^{3} = \frac{1}{4} \times {(2.1)}^{2} \times (8.4)$
$= {(2.1)}^{3}$
or $R = 2.1 c m$

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