The radii of three metal spheres are 3 ,cm, 4 | vedclass

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(D) The volume of a sphere is given by the formula $V = \frac{4}{3} \pi r^3$.Let the radii of the three spheres be $r_1 = 3 \,cm, r_2 = 4 \,cm$,and $r

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$6$

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

The radii of three metal spheres are $3 \,cm, 4 \,cm$ and $5 \,cm$ respectively. They are melted into a single solid sphere. Find the radius of the new solid sphere (in $cm$).

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