Question

two right circular cylinders of equal volume have their heights in the ratio 1:2,what is the tatio of their radii?

Answer 1

Answer:

Step-by-step explanation:

Let two cylinders be of the form as attached

Then According to Question,

∴π(R')²2H = πR²H

∴(R'/R)² = πH/π2H 

∴ (R'/R)² = 1/2

∴R'/R = 1/√2

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Answer 2

Given:

Let the radius of the base of two right circular cylinders be R & r.

Let the Height of the base of two right circular cylinders be H & h.

Ratio of Height  of two right circular cylinders =  H : h = 1 : 2 i.e H/h = 1/2

Volume of two right circular cylinders are  equal , therefore

V1 = V2

πR²H = πr²h

R²H = r²h

R²/r² = h/H

(R/r)² = h/H

(R/r)² = 2/1

(R/r) = √2/1

R : r = √2 : 1

Hence, the the ratio of their radii is R : r = √2 : 1 .