Question

the volume and the height of cylinder and cone are equal.find theratio of the radii of their bases

Answer 1

given that ,Πr²h= 1/3Πr²h
= 1= 1/3
ratio= 1/3÷ 1
= 1:3

Answer 2

Naming or nomenclature

Let volume of cylinder be V₁

Let volume of cone be V₂

Let radius of cylinder be r₁

Let radius of cone be r₂

Let height of cylinder be h₁

Let height of cone be h₂

Volume of cones and cylinders

Volume of cone = 1/3 π r² h

                           = 1/3 π r₂² h₂

Volume of cylinder = π r² h

                                = π r₁² h₁

V₁ = V₂

==> 1/3 π r₂²h₂ = π r₁² h₁

Cancel π both sides :

==> 1/3 r₂²h₂ = r₁² h¹

Cancel h both sides as h₂ = h₁

==> 1/3 r₂² = r₁²

==> r₁² / r₂² = 1 / 3

Take square root both sides :

==> r₁ / r₂ = 1 / √3

ANSWER :

The radii are in the ratio 1 : √3