Volume Ratio From Surface Ratio

If you could answer this question for me and tell me how you got your answer that would be very helpful. The surface areas of two similar figures are 16insquared and 25insquared the volume of the larger figure is 500incubed what is the volume of the smaller figure?
- James (age 16)
Austin

The volume of an object grows as the cube of its characteristic length dimension.   The surface grows only as the square.   If the two objects are similar in shape and if you know the ratio of the surfaces then V₁/V₂ =  (S₁/S₂)^3/2.  In your case, 500x (16/25)^3/2 = 500x64/125 = 256.

LeeH

(published on 07/15/2011)