Question

two rectangular prisms have the same volume. the area of the base of the blue prism is 4 1/8 square units. the area of the red prism is one-half that to the blue prism. which statement is true?

Answer 1

Given are two prisms, Blue and Red prisms.

Given the Base of Red prism is half the base of Blue prism.

We know the formula for volume of any prism is given by :-

volume = base area × height

$Volume\;\; of\;\; Blue\;\; prism = Volume\;\; of\;\; Red\;\; prism\\\\ V_{Blue} =V_{Red} \\\\ (Base_{Blue}) (Height_{Blue})=(Base_{Red}) (Height_{Red})\\\\(Base_{Blue}) (Height_{Blue})=(\frac{1}{2}\;Base_{Blue}) (Height_{Red})\\\\ (Height_{Blue})=(\frac{1}{2}) (Height_{Red})\\\\ (2)(Height_{Blue})=(Height_{Red})$

So, the height of Red prism is twice the height of Blue prism.