Given the areas and volumes of two similar (i.e. one is the perfect enlargement of the other one) objects, one which has been enlarged and the other not. We can determine one of the objects area or volume given enough information.

Example: Cuboids A and B are similar. The surface area of A is 25cmand that of B is 400cm2. Given that the volume of A is  210cm3, find the volume of B.

So gathering all the information we know.(SA = surface area, V = volume)

A: SA = 25cm2 , V= 210cm3 

B: SA= 400cm2. V= ? 

Since both shapes are similar, we can find the Scale Factor(SF) between both shapes. To do this we divide the surface area of B by that of A => 400*25 = 16. So 16 is the Surface area Factor (= SF2) to get the Volume Factor (=SF3we first need to take the square root of 16 (to find the Scale factor) , then cube it. i.e. 161/2=4 => 43 = 64. The volume of B is then 210*64 = 13440cm3

Remember, If you're given the surface area of two objects that are similar:

  • Linear factor is just the Length x SF
  • The Surface Area factor is just the Surface area x SF2
  • The Volume factor is just the Volume x SF3


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