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Some info about the surface area and volume of the two similar solids has been given....

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user4481582 | eNoter

Posted May 5, 2013 at 7:54 PM via web

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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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tiburtius | High School Teacher | (Level 3) Associate Educator

Posted May 5, 2013 at 8:29 PM (Answer #1)

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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

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