Answer:
D)The height of the red prism is three times the height of the blue prism
Explanation:
Here is the complete question
Two rectangular prisms have the same volume. The area of the base of the blue prism is 2 1/6 square units. The area of the base of the red prism is one third that of the blue prism.
which statement is true?
a)The height of the red prism is one-third the height of the blue prism
B)The height of the red prism is the same as the height of the blue prism
C)The height of the red prism is six times the height of the blue prism.
D)The height of the red prism is three times the height of the blue prism
Solution
Since both prisms have the same volume, V = A₁h₁ = A₂h₂ where A₁ and A₂ are the areas of the red and blue prisms respectively and h₁ and h₂ are the heights of the red and blue prisms respectively. For the question, A₁ = A₂/3. Substituting this into the equation, A₁h₁ = A₂h₂
A₂h₁/3 = A₂h₂
h₁ = 3h₂ . So the height of the red prism is thee times the height of the blue prism.