Asked by Anonymous

I have two mathematically similar shapes, one of which has a volume of 1 litre and one which has a volume of half a litre. If the largest shape has a height of 40 cm, what (in centimetres) is the height of the smaller shape?
Answered by mathhelper
The volumes of similar shapes are proportional to the cubes of their corresponding sides, so

1 L / .5 L = 40^3 cm^3 / s^3 cm^3
cancelling the units
1 / .5 = 40^3/s^3
s^3 = .5(64,000) = 32,000
s = 32000^(1/3) = appr 31.748 cm

check"
40^3 : 31.748^3
= 64000 : 32000
= 2 : 1
Answered by oobleck
the ratio of volumes is the cube of the ratio of heights.
So the ratio of heights is 1:∛2
40/∛2 = 31.748
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