Answer:
1: 8
Step-by-step explanation:
Volume of a cylinder(V) is given by:
[tex]V = \pi r^2h[/tex]
where,
r is the radius and h is the height of the cylinder.
As per the statement:
Let V and V' be the volume of small cylinder and large cylinder.
The small cylinder has a volume of 54π cm^3.
⇒[tex]V =54 \pi cm^3= pi r^2h[/tex] ....[1]
It is also given:
In a similar cylinder, the dimensions have been doubled
[tex]r' = 2r[/tex] and [tex]h' = 2h[/tex]
then, volume for large cylinder we get;
[tex]V' = \pi (2r)^2(2h) = 8 \pi r^2h[/tex]
⇒[tex]V' = 8V[/tex]
⇒[tex]\frac{V}{V'} = \frac{1}{8}[/tex]
⇒V : V' = 1 : 8
Therefore, the ratio of the volumes (small to large) is, 1: 8
