Ratio of Base Area of 2 Similar Prisms from the Volumes or Ratio of Heights

Question

I have a math question that states:

"The volumes of two similar prisms are 512 ft³ and 8000 ft³.

A. Find the ratio of their heights.

B. Find the ratio of the area of their bases."

For A, I got ³√(⁵¹²/₈₀₀₀)=²/₅

Is A correct??

My main question is that I don't know how to find B.

Please help me!! Thanks!

Answer 1

If two shapes are similar , their corresponding parts such as radius or heights are proportional. so for two similar prisms with h₁ and h₂ , sides s₁ and s₂

h₁/h₂=s₁/s_2. In addition, if two 3-d shapes are similar, then their volumes will be proportional to the cube of their corresponding sides. So if you take the cube root of given ratio which is 512/8000, you get 2/5.The ratio between the areas of two similar shape is equal to the square of the similarity ratio which is going to be square of 2/5=4/25