EXPLANATION
The radius of a cone is given by the following relationship:
[tex]\text{Volume}=\frac{1}{3}\cdot\pi\cdot r^2\cdot h[/tex]We have Volume=V= 2,110.08 cm^3 and the height is h=14cm
Replacing terms:
[tex]2,110.08=\frac{1}{3}\cdot\pi\cdot r^2\cdot14[/tex]Multiplying both sides by 3:
[tex]2,110.08\cdot3=\pi\cdot r^2\cdot14[/tex]Dividing both sides by 14*pi:
[tex]\frac{2,110.08\cdot3}{14\cdot\pi}=r^2[/tex]Applying the square root to both sides:
[tex]\sqrt[]{\frac{2,110.08\cdot3}{14\cdot\pi}}=r[/tex]Switching sides:
[tex]r=\sqrt[]{\frac{2,110.08\cdot3}{14\cdot3.14}}[/tex]Simplifying:
[tex]r=\sqrt[]{144}[/tex]Simplifying:
[tex]r=12[/tex]The answer is r=12 centimeters
