If a liquid from a completely filled spherical container of inner radius r is poured into a cube shaped container, what would be the dimensions of the cube in terms of the radius of the sphere?

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1 Answer
Sep 28, 2017

root(3)(36pi)/3r

Explanation:

Volume of cube is equal to volume of sphere.

Volume of a sphere: V = 4/3pir^3

Let a be a side of the cube.

Then:

a^3 = volume of cube.

So we have:

Volume of cube = volume of sphere:

a^3 = 4/3pir^3

We need to manipulate 4/3pir^3 to get the required result.

Since 4/3pir^3 can be expressed (4pir^3)/3 This is just a fraction like any other, so we can multiply numerator and denominator by 9

This then gives:

(36pir^3)/27

Now we have:

a^3 = (36pir^3)/27

Taking cube roots:

root(3)(a^3) = root(3)((36pir^3)/27) => root(3)(a^3) = (root(3)(36pir^3))/(root(3)(27))

Extracting and evaluating any cubes:

a = (rroot(3)(36pi))/3

Which can be expressed:

a = (root(3)(36pi))/3r