For this case we have that by definition, the volume of a cone is given by:
[tex]V = \frac {1} {3} * \pi * r ^ 2 * h[/tex]
Where:
r: It is the radius of the cone
h: It is the height of the cone
According to the statement data we have:
[tex]h = 12 \ cm\\V = 125 \ cm ^ 3[/tex]
Substituting in the formula:
[tex]125 = \frac {1} {3} * \pi * r ^ 2 * 12[/tex]
We cleared the radius:
[tex]3 * 125 = \pi * r ^ 2 * 12\\\frac {3 * 125} {12 \pi} = r ^ 2\\9.9522 = r ^ 2\\r = \pm \sqrt {9.9522}[/tex]
We choose the positive value:
[tex]r = 3.1547[/tex]
We round and we have that the radius of the cone is:
[tex]r = 3.16 \ cm[/tex]
ANswer:
[tex]r = 3.16 \ cm[/tex]
