Question

Calculate the radius of the sphere with the given volume.
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​ Volume=4/81π ft^3

Answer 1

(∛3)/2 ft = r

Explanation:

Start with the formula for the volume of a sphere: V = (4/3)πr³. Solve this for r³ and then take the cube root of the result:

3V

V = (4/3)πr³ => (3/4)V = πr³ => (------- = r³

4π

3 · 4/81π ft^3 3 · 4π ft³ 3 ft³

Here we have r³ = -------------------- = ---------------- = -------------

4π 8(4π) 8

and so the radius is r = ∛[ (3/8) ft³] = (∛3)/2 ft = r