Percentage, Volume

Question

A food company distributes its tomato soup in two cans of different sizes. For the larger can, both the diameter and the height have been increased by
25%
.

By what percentage does the volume of the can increase from the smaller can to the larger can? Round your answer to the nearest percent.

Answer 1

Volume = π(radius)²(height) for cylindrical cans.

 

 

For the relationship between large (R, H, V) and small cans (r, h, v) we can write

 

R = (1 + 25%)r = 1.25r

 

H = (1 + 25%)h = 1.25h

 

 

The volume of the small can is v = πr²h and the volume of the large can is V = πR²H.

 

 

V can be written in terms of r, h, and v:

 

V = π(1.25r)²(1.25h) = (1.25)³πr²h = 1.25³v = 1.953 v

 

 

The volume of the larger can is (1.953v - v)/v x 100% = 95.3% more than the volume of the smaller can or almost twice the volume.