Answer:
Radius = 3 units
Step-by-step explanation:
The volume of the cone is equal to [tex]18\pi[\tex] cubic units.
Also given that diameter is equal to height. Hence h = 2r
Volume of cone is given as
[tex]V=\frac{1}{3}\pi r^2h[\tex]
[tex]V=\frac{1}{3}\pi r^2(2h)[\tex]
Given
[tex]V = 18\pi[\tex]
[tex]18\pi=\frac{2}{3}\pi r^3[\tex]
[tex]18=\frac{2}{3}r^3[\tex]
[tex]r^3=\frac{3}{2} \times 18[\tex]
[tex]r^3=27[\tex]
[tex]r=3[\tex]
And hence radius is 3 units.