The radius of the cone is 2 inches.
The volume of cone:
The volume of a cone is determined by the amount of space occupied by the cone. A three-dimensional figure having a single circular base is known as a cone. The base and the vertex are connected by a curved surface. A cone with a radius of r has a volume V that is one-third the area of the base B times the height h.
[tex]V=\frac{1}{3} \pi r^{2} h[/tex] or [tex]V=\frac{1}{3} Bh[/tex],
Since, [tex]B=\pi r^{2}[/tex]
How to determine the volume of cone?
Given that the volume of cone V is 48π cubic inches and Height of the cone h=36 inches.Volume of cone [tex]V=\frac{1}{3} \pi r^{2} h[/tex] -------1
Here, the base of the cone is circular in shape and the area of circle is [tex]\pi r^{2}[/tex]. Consider [tex]B=\pi r^{2}[/tex]
Substituting the area of base in the equation (1).
[tex]V=\frac{1}{3} \pi r^{2}[/tex]
[tex]= \frac{1}{3} Bh[/tex]
Substitute the given values in the equation (1).
⇒ [tex]48\pi =\frac{1}{3} \pi r^{2} 36[/tex]
⇒ [tex]\frac{48\pi }{36\pi } =\frac{r^{2} }{3}[/tex]
⇒ [tex]\frac{12(3)}{9}=r^{2}[/tex]
⇒[tex]4=r^{2}[/tex]
⇒ [tex]r=2[/tex]
Thus, the radius of the cone is 2 inches.
Learn more about cone here- https://brainly.com/question/1315822 #SPJ2
