If three metallic spheres of radii 6, cm,8, c | vedclass

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(B) When spheres are melted to form a new sphere,the volume remains conserved.Let the radii of the three spheres be $r_1 = 6\, cm$,$r_2 = 8\, cm$,and

Vedclass · Accepted Answer

$24$

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(B) When spheres are melted to form a new sphere,the volume remains conserved.Let the radii of the three spheres be $r_1 = 6\, cm$,$r_2 = 8\, cm$,and $r_3 = 10\, cm$.Let the radius of the new sphere be $R$.The volume of a sphere is given by $V = \frac{4}{3}\pi r^3$.Equating the sum of the volumes of the three spheres to the volume of the new sphere:$\frac{4}{3}\pi R^3 = \frac{4}{3}\pi r_1^3 + \frac{4}{3}\pi r_2^3 + \frac{4}{3}\pi r_3^3$$R^3 = r_1^3 + r_2^3 + r_3^3$$R^3 = 6^3 + 8^3 + 10^3$$R^3 = 216 + 512 + 1000 = 1728$$R = \sqrt[3]{1728} = 12\, cm$.The diameter of the new sphere is $D = 2R = 2 	imes 12 = 24\, cm$.

If three metallic spheres of radii $6\, cm$,$8\, cm$,and $10\, cm$ are melted to form a single sphere,the diameter of the new sphere will be (in $cm$)?

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