Question

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

Answer 1

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Let volume of heavier sphere be $V_{1}$
& volume of lighter sphere be $V_{2}$

Let radii of heaviersphere be $r_{1}$
& radii of lighter sphere be $r_{2}$

Given,

Weight of heavier sphere= 5920 g
& weight of lighter sphere = 740 g

We have,
$weight = density × Volume$

So
$\frac{Weight\: of\: heavier\: sphere}{weight\: of\: lighter\: sphere}$ = $\frac{density×V_{1}}{density×V_{2}}$

As sphere is made of same metal,

$\frac{Weight\: of\: heavier\: sphere}{weight\: of\: lighter\: sphere} = \frac{V_{1}}{V_{2}}$

$\frac{5920}{740} = \frac{\frac{4}{3}×\pi×r_{1}^{3}}{\frac{4}{3}×\pi×r_{2}^{3}}$

$8= \frac{r_{1}^{3}}{r_{2}^{3}}$

Given $d_{2}=5$
=> $r_{2}=\frac{5}{2}$

$r_{1}^{3} = (\frac{5}{2})^{3}×8$

$r_{1}^{3} = 125$

$r_{1} = 5$

Hence,
The radius of larger sphere is 5 cm ✓✓✓

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Answer 2

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