The ratio of the volumes of two similar circular cylinders is 27:64. What is the ratio of the

diameters of their similar bases?

The ratio of their bases = 3√3 : 8

Step-by-step explanation:

Given,

The ratio of the volume of two cylinders is 27:64.

To find the ratio of the diameters of the cylinders of their base.

Formula

Let, the radius and height of a cylinder is r and h. The volume of the cylinder V = πr²h

Let,

Radius of cylinder 1 is R and the radius of the cylinder 2 is r.

The height of the both cylinder is h.

According to the problem,

πR²h = 27a and πr²h = 64a

So,

πR²h : πr²h = 27a:64a

or, R²:r² = 27:64

or, R:r = 3√3 : 8

Hence,

The ratio of their bases = 3√3 : 8