Question

The ratio of the radii of two cylinders of equal height is 9: 4 then the ratio of its volume is _____​

Answer 1

81 : 16

Solution:

We are given that ratio of radii of two cylinders of equal height is 9 : 4. We need to find the ratio of cylinder's volume.

From the question, we can observe that:

• r₁ / r₂ = 9 / 4
• h₁ = h₂

We know that, the formula to find volume of cylinder is πr²h. Since, we need to find the ratio of their volumes, let us divide π(r₁)²h by π(r₂)²h to get the ratio.

⟹ V₁ / V₂ = π(r₁)²h / π(r₂)²h

[ π and h gets cancelled since their values are equal ]

⟹ V₁ / V₂ = (r₁)² / (r₂)²

⟹ V₁ / V₂ = (9)² / (4)²

⟹ V₁ / V₂ = 81 / 16

⟹ V₁ : V₂ = 81 : 16

Hence, the ratio of cylinder's volume is 81 : 16.