# Two rectangular prisms have the same volume. the area of the base of the blue prism is 418 square units. the area of the

2 answers

###### Question:

Two rectangular prisms have the same volume. the area of the base of the blue prism is 418 square units. the area of the base of the red prism is one-half that of the blue prism. which statement is true?

## Answers

its 2 times the amount of the blue prism.

Volume of prism = Area of cross-section × height

Volume of blue prism = ([tex]4 \frac{1}{8}[/tex])×([tex]h_B[/tex]

Volume of red prism = [tex]( \frac{1}{2})(4 \frac{1}{8})[/tex]×[tex](h_R)[/tex]

[tex]V_{blue}:V_{red}[/tex]

[tex](4 \frac{1}{8})(h_B):( \frac{33}{16})(h_R)[/tex]

[tex]\frac{33}{8}h_B: \frac{33}{16}h_R[/tex]

[tex]\frac{66}{16}h_B: \frac{33}{16}h_R[/tex]

[tex]66h_B:33h_R[/tex]

[tex]66h_B = 33h_R[/tex]

[tex]\frac{66}{33}= \frac{h_R}{h_B}[/tex]

[tex]\frac{2}{1}= \frac{h_R}{h_B}[/tex]

[tex]2:1=h_R:h_B[/tex]

The height of red prism is twice the height of the blue prism

Correct option: B

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