Two solid spheres made of the same metal have weights of 5920 gm and 740 gm. If the diameter of the smaller sphere is 5 cm, then the radius of the larger sphere will be

Two solid spheres are made of the same metal with weights of 5920 gm and 740 gm. The diameter of the smaller sphere is 5 cm.

The radius of the smaller sphere:

$r = \dfrac{5}{2} = 2.5$ cm

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Both spheres are made of the same metal, so they have the same density. The ratio of weights equals the ratio of volumes.

$\dfrac{\text{Weight}_1}{\text{Weight}_2} = \dfrac{\text{Volume}_1}{\text{Volume}_2}$

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$\dfrac{5920}{740} = \dfrac{\text{Volume of larger sphere}}{\text{Volume of smaller sphere}}$

$\dfrac{5920}{740} = 8$

Volume of larger sphere $= 8 \times$ Volume of smaller sphere

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The volume of a sphere is $\dfrac{4}{3}\pi r^3$.

For radius $R$ of the larger sphere and $r = 2.5$ cm of the smaller sphere:

$\dfrac{4}{3}\pi R^3 = 8 \times \dfrac{4}{3}\pi r^3$

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$R^3 = 8 \times r^3$

$R^3 = 8 \times (2.5)^3$

$R^3 = 8 \times 15.625$

$R^3 = 125$

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$R = \sqrt[3]{125}$

$R = 5$ cm

The radius of the larger sphere is $5$ cm.