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(D) The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$.When three spheres are melted and recast into a new sphere,the total volu

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$6$

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(D) The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$.When three spheres are melted and recast into a new sphere,the total volume remains conserved.Let the radii of the three spheres be $r_1 = 3 \, cm$,$r_2 = 4 \, cm$,and $r_3 = 5 \, cm$.Let the radius of the new sphere be $R$.The total volume of the three spheres is $V_{total} = \frac{4}{3} \pi (r_1^3 + r_2^3 + r_3^3)$.The volume of the new sphere is $V_{new} = \frac{4}{3} \pi R^3$.Equating the volumes: $\frac{4}{3} \pi (3^3 + 4^3 + 5^3) = \frac{4}{3} \pi R^3$.$R^3 = 3^3 + 4^3 + 5^3 = 27 + 64 + 125 = 216$.$R = \sqrt[3]{216} = 6 \, cm$.

The radii of three metallic spheres are $3 \, cm$,$4 \, cm$,and $5 \, cm$. These spheres are melted and recast into a single new sphere. Find the radius of the new sphere (in $cm$).

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