   SEARCH HOME Math Central Quandaries & Queries  Question from mike: what is the % difference between a 3 inch diameter pipe compared to a 4 inch diameter pipe? and how do i find the answer? Mike,

The subject line of your email was "volume differences" so I am going to assume you are looking at the percentage difference in the volumes. The volume of a cylinder is π × (d/2)2 × h where d is the inside diameter, h is the length and π is approximately 3.1416. Thus for two pipes of the same length h then the volumes are

π × (3/2)2 × h = 9/4 × π × h

and

π × (4/2)2 × h = = 16/4 × π × h

for a difference of

5/4 × π × h cubic units.

If you want the difference as a percentage you need to ask "percentage of what?"

As a percentage of the 3 in diameter pipe

(5/4 × π × h)/(9/4 × π × h) × 100 = 5/9 × 100 = 55.56%

so the 4 inch diameter pipe has a volume which is 55.6% larger than the volume of the 3 inch diameter pipe.

As a percentage of the 4 in diameter pipe

(5/4 × π × h)/(16/4 × π × h) × 100= 5/16 × 100 = 31.25%

so the 3 inch diameter pipe has a volume which is 31.25% smaller than the volume of the 4 inch diameter pipe.

Percentages can be confusing,
Penny     Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.