How is the ratio of the volumes related to the ratio of corresponding dimensions

Question

A cylinder has a radius of 3 cm and a length of 10 cm. Every dimension of the cylinder is multiplied by 3 to form a new cylinder. How is the ratio of the volumes related to the ratio of corresponding dimensions?

Answer 1

"ratio of the volumes related to the ratio of corresponding dimensions"

 

 Let:

    r = 3 cm      [dimension of small cylinder]

    h = 10 cm    [dimension of small cylinder]

 

So,

   3*3=9 cm   [radius of large cylinder]

   3*10=20cm    [height of large cylinder]

 

You may calculate the volumes to check the answer.

 

However, the ratio does not depend on the dimensions.

Volume = πr²h

Ratio of volumes:  π(3r)²(3h) / πr²h  =  27πr²h / πr²h = 27 times [that is, 3³] as much.