Question

the height of two cylinders are in the ratio 5:3 and their volume are in the ratio 20:27 then find the ratio of their radii.

Answer 1

Here's ur answer
Solution

Let radii be 2r and 3r respectively
and height be 5h and 3h respectively 
Volume ratio = Pi*(2r)^2 5h / Pi*(3r)^2 3h = 20:27
Curved surface area ratio = 2 Pi*(2r) 5h / 2 Pi*(3r) 3h = 10:9


Hope it helpful

Answer 2

Volume of a Cylinder is given by : π × (Radius)² × (Height)

It Means the Volume of a Cylinder is Directly Proportional to its Square of Radius and Height of Cylinder

Let the Volume of the First Cylinder be : V₁

Let the Volume of the Second Cylinder be : V₂

Let the Radius of the First Cylinder be : R₁

Let the Radius of the Second Cylinder be : R₂

Let the Height of the First Cylinder be : H₁

Let the Height of the Second Cylinder be : H₂

$\mathsf{\implies \dfrac{V_1}{V_2} = (\dfrac{R_1}{R_2})^2(\dfrac{H_1}{H_2})}$

Given - The Ratio of Volumes of the Two Cylinders as 20 : 27

Given - The Ratio of Height of the Two Cylinders as 5 : 3

$\mathsf{\implies \dfrac{20}{27} = (\dfrac{R_1}{R_2})^2(\dfrac{5}{3})}$

$\mathsf{\implies (\dfrac{R_1}{R_2})^2 = (\dfrac{4}{9})}$

$\mathsf{\implies \dfrac{R_1}{R_2} = \sqrt{\dfrac{4}{9}}}$

$\mathsf{\implies \dfrac{R_1}{R_2} = \dfrac{2}{3}}$

The Ratio of their Radii is 2 : 3