# Some info about the surface area and volume of the two similar solids has been given. Find the missing value. Solid 1 SA=1088 km2 V=13312 km3 Solid 2 SA= 425 km2 V=?

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### 1 Answer

Let `k` be the scale factor between two objects. If `l_1,A_1` and `V_1` are length, area and volume of one object and `l_2,A_2` and `V_2` are length area and volume of other similar object, then the following formulas hold:

`l_1=kl_2` **(1)**

`A_1=k^2A_2` **(2)**

`V_1=k^3V_2` **(3)**

Hence from (2) we get

`k^2=A_1/A_2=1088/425=2.56`

`k=1.6`

`k^3=4.096`

Now from (3) we get

`13312=4.096V_2`

`V_2=13312/4.096=3250"km"^3` **<-- Your solution**