Answer:
It is given that the volume of a cone = [tex]3\pi x^3[/tex] cubic units
Volume of cone with radius 'r' and height 'h' = [tex]\frac{1}{3}\pi r^2h[/tex]
Equating the given volumes, we get
[tex]3\pi x^3=\frac{1}{3}\pi r^2h[/tex]
[tex]r^2h=3[/tex] × [tex]3x^3[/tex]
[tex]r^2h=9 x^3[/tex]
It is given that the height is 'x' units.
Therefore, [tex]r^2x=9x^3[/tex]
[tex]r^2=9x^2[/tex]
Therefore, [tex]r=3 x[/tex]
So, the expression '[tex]3 x[/tex]' represents the radius of the cone's base in units.
