Question

Ratio of the radii of the cylinder to the cone is 1:2. Assume, their heights are the same. Find the ratio of their volumes?

Answer 1

Answer:

Let the radius of the cylinder be x

The radius of the cone is 2x

Let the common height be h

Find the volume of the cylinder:

Volume = πr²h

Volume = πx²h

Find the volume of the cone:

Volume = 1/3 πr²h

Volume = 1/3 π(2x)² h

Volume = 4/3 πx²h

Find the volume of the cone:

Volume = 1/3 πr²h

Volume = 1/3 π(2x)² h

Volume = 4/3 πx²h

Find the ratio:

Volume of cylinder : Volume of cone = πx²h : 4/3 πx²h

Divide both sides by πx²h:

Volume of cylinder : Volume of cone = 1 : 4/3

Multiply both sides by 3:

Volume of cylinder : Volume of cone = 3 : 4

_______✔

Answer 2

Answer:

Let. ri&hi are the radius &height of cylinder

r2 &h2 are the radius & height of cone

Vi and v2 are the volumes of cylinder and cone

VI : V2= πr 1 ^2 h1:1/3πr^2h 2

V1: v2 = πI^2 xl: I/3πx2^2 x I

V1:V2 =I:4/3

V1:V2 = 3;4