Question

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

Answer 1

Answer:

(∛3)/2 ft =  r

Step-by-step 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