Let's call the radius of the base of the cone "r". The volume of the cube is (5 cm)^3 = 125 cm^3. The volume of the cone is given by the formula (1/3)πr^2h, where h is the height of the cone, which is 3 cm. Setting these two volumes equal to each other, we have:
(1/3)πr^2 * 3 = 125
Expanding and solving for r, we have:
πr^2 * 3 = 375
πr^2 = 375 / 3 = 125
r^2 = 125 / π
r = √(125 / π)
So the exact value of the radius of the base of the cone is approximately equal to √(125 / π) cm