If the volume of a sphere is equal to the volume of a hemisphere then, what is the relationship between the radius of the sphere to the radius of the hemisphere?
[ Conside $r_{1}$ as radius of sphere and $r_{2}$ as radius of hemisphere ]

2 (r_{1})^{3} = (r_{2})^{3}

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4 (r_{1})^{3} = (r_{2})^{3}

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2 (r_{1})^{3} = 3 (r_{2})^{3}

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2 (r_{1})^{3} = 4 (r_{2})^{3}

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Solution

The correct option is A $2 (r_{1})^{3} = (r_{2})^{3}$

Given that,
Volume of sphere = volume of hemisphere
Radius of sphere = $r_{1}$
Radius of hemisphere = $r_{2}$

We know that,
Volume of sphere
$= \frac{4}{3} π r^{3}$

$= \frac{4}{3} π (r_{1})^{3}$

Volume of hemisphere
$= \frac{2}{3} π r^{3}$

$= \frac{2}{3} π (r_{2})^{3}$

Now,
$\frac{4}{3} π (r_{1})^{3} = \frac{2}{3} π (r_{2})^{3}$
$\Rightarrow \frac{4}{3} (r_{1})^{3} = \frac{2}{3} (r_{2})^{3}$
$\Rightarrow 2 (r_{1})^{3} = (r_{2})^{3}$

Hence, the relation between radius of sphere to radius of hemisphere is $2 (r_{1})^{3} = (r_{2})^{3}$ .

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