Respuesta :
36in^3
as the volume of a cone is 1/3 that of the volume of a cylinder the smallest cylinder that the cone can fit inside of is one that is exactly 3x its the volume
as the volume of a cone is 1/3 that of the volume of a cylinder the smallest cylinder that the cone can fit inside of is one that is exactly 3x its the volume
Answer:
The correct option is 3.
Step-by-step explanation:
It is given that the volume of a cone is 12 cubic inches.
The volume of a cone is
[tex]V_1=\frac{1}{3}\pi r^2h[/tex]
Put V₁=12 in the value equation.
[tex]12=\frac{1}{3}\pi r^2h[/tex]
Multiply both sides by 3.
[tex]36=\pi r^2h[/tex] .... (1)
Where, r is radius of base, h is height.
It is given that the cone fits exactly inside of the cylinder. It means the height and the radius of the cylinder is same.
The volume of a cylinder is
[tex]V_2=\pi r^2h[/tex]
Using equation (1) we get
[tex]V_2=36[/tex]
The volume of cylinder is 36 cubic inches. Therefore the correct option is 3.
