Two solid spheres made of the same metal have weights $5920$ g and $740$ g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is $5$ cm.

12

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Solution

The correct option is D $5$ cm
Mass is directly proportional to volume for same metal (Density)
Let Mass of Solid 1 be $M_{1}$ , Volume be $V_{1}$ , Mass of Solid 2 be $M_{2}$ and Volume be $V_{2}$
Now $\frac{M_{1}}{M_{2}} = \frac{V_{1}}{V_{2}}$
Volume of sphere is directly proportional to $R^{3}$
So, $\frac{M_{1}}{M_{2}} = \frac{V 1}{V 2} = \frac{R_{1}^{3}}{R_{2}^{3}}$
$\Rightarrow \frac{5920}{740} = \frac{R_{1}^{3}}{R_{2}^{3}}$
$\Rightarrow \frac{R_{1}^{3}}{R_{2}^{3}} = 8$
$\Rightarrow \frac{R_{1}}{R_{2}} = \sqrt[3]{8}$
$\Rightarrow \frac{R_{1}}{R_{2}} = 2$
So, $R_{1} = R_{2} \times 2$
So, $R_{1} = 2.5 \times 2 = 5$

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Two solid spheres made of the same metal have weights 5920 g and 740 g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is 5 cm.

Two solid spheres made of the same metal have weights $5920$ g and $740$ g, respectively. Determine the radius of the larger sphere, if the diameter of the smaller one is $5$ cm.