Three solid spheres have their radii r_{1}, r | vedclass

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(C) When objects are melted and recast,the total volume remains constant.Let the radius of the new sphere be $R$.The volume of a sphere is given by th

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$(r_{1}^{3} + r_{2}^{3} + r_{3}^{3})^{1/3}$

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(C) When objects are melted and recast,the total volume remains constant.Let the radius of the new sphere be $R$.The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^{3}$.The sum of the volumes of the three smaller spheres is equal to the volume of the new larger sphere:$\frac{4}{3} \pi r_{1}^{3} + \frac{4}{3} \pi r_{2}^{3} + \frac{4}{3} \pi r_{3}^{3} = \frac{4}{3} \pi R^{3}$Dividing both sides by $\frac{4}{3} \pi$,we get:$r_{1}^{3} + r_{2}^{3} + r_{3}^{3} = R^{3}$Taking the cube root on both sides,the radius of the new sphere is:$R = (r_{1}^{3} + r_{2}^{3} + r_{3}^{3})^{1/3}$

Three solid spheres have their radii $r_{1}, r_{2}$ and $r_{3}$. The spheres are melted to form a single solid sphere of a bigger radius. The radius of the new sphere is:

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