Two cylinders of equal volume have heights in the ratio 1:16. The ratio of their radii is?

Given:

Two cylinders have equal volumes.

The ratio of their heights is 1 : 16.

Formula used:

Volume of a cylinder = πr²h

Calculation:

Let the heights of the two cylinders be h₁ and h₂, and their radii be r₁ and r₂ respectively.

Given that the ratio of their heights is 1 : 16, let h₁ = h and h₂ = 16h.

Given that the volumes are equal:

πr₁²h₁ = πr₂²h₂

⇒ r₁²h₁ = r₂²h₂

⇒ r₁²(h) = r₂²(16h)

⇒ r₁² = 16r₂²

Taking the square root of both sides:

⇒ r₁ = 4r₂

⇒ r₁/r₂ = 4/1

∴ The ratio of their radii is 4 : 1.