I forgot my radii! 2

Geometry Level 1

I have two spheres with different sizes. The radius of the larger sphere is $R$ and the radius of the smaller sphere is $r$ . Given that the volume of the larger sphere is twice the volume of the smaller sphere, find the value of $\dfrac Rr$ .

I forgot my radii!

Cannot be determined

\sqrt[3]{2}

\sqrt{2}

1 solution

Ethan Mandelez
Dec 5, 2020

The volume of a sphere is $\frac{4}{3}πa^3$ , where $a$ is the radius. From the information given above:

$2\times\frac{4}{3}πr^3 = \frac{4}{3}πR^3$

$\frac{8}{3}πr^3 = \frac{4}{3}πR^3$

$\left(\dfrac {R^3}{r^3} \right) = 2$

Hence $\left(\dfrac {R}{r} \right) = \boxed{\sqrt[3]{2}}$

I forgot my radii! 2

1 solution

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