Answer:
Ratio of their heights is 8 ft and 20 ft.
Step-by-step explanation:
It is given the volumes of similar prisms are 512 ft^3 and 8000 ft^3,
Please remember the concept if two shapes are similar and their sides are in the ratio a:b
Then their area is in the ratio of [tex]a^{2} :b^{2}[/tex]
And their volume is in the ratio of [tex]a^{3} :b^{3}[/tex]
So, if we take cube root of the given volumes it would give us the ratio of heights.
So, ratio of heights of similar shapes =[tex]\sqrt[3]{512} :\sqrt[3]{8000}[/tex]
Simplify them.
So, ratio of heights =8 : 20
