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Question

 A cylinder with radius 7 in. and height 6 in. has its radius tripled. How many times greater is the volume of the larger cylinder than the smaller cylinder? Use pencil and paper. Explain how the volume of the cylinder changes if its height were also tripled.
The volume of the larger cylinder is
nothing times greater than the smaller cylinder.

Answer 1

Before tripling the radius,

 

V = πr²h

 

After tripling the radius,

 

V' = π(3r)²h = 9πr²h = 9V

 

The volume increased by a factor of 9.  Similarly, you can show that if you triple the height, the volume increases by a factor of 3.