Question

The volumes of two similar prisms are 512 ft³ and 8000 ft³. Find the ratio of their heights.

Answer 1

Ratio of their heights is 8 ft and 20 ft.

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
`a^(2) :b^(2)`

And their volume is in the ratio of
`a^(3) :b^(3)`

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 =
`\sqrt[3]{512} :\sqrt[3]{8000}`

Simplify them.

So, ratio of heights =8 : 20