Question

question 4 (multiple - choice, worth 2 points) the cross - section of rectangular prism a measures 6 units by 4 units. the cross - section of triangular prism b has a base that measures 8 units and a height of 6 units. if the length of each prism is 7.22 units, which statement is true? volume a = volume b volume a = 1/3(volume b) volume a = 2(volume b) volume a = 1/2(volume b)

Explanation:

Step1: Calculate volume of rectangular prism A

The cross - sectional area of rectangular prism A is $A_{A}=6\times4 = 24$ square units. The volume formula for a prism is $V = A\times l$, where $A$ is the cross - sectional area and $l$ is the length. Given $l = 7.22$ units, so $V_{A}=24\times7.22=173.28$ cubic units.

Step2: Calculate volume of triangular prism B

The cross - sectional area of triangular prism B: The area of a triangle is $A=\frac{1}{2}\times base\times height$. Here, base = 8 units and height = 6 units, so $A_{B}=\frac{1}{2}\times8\times6=24$ square units. Using the volume formula $V = A\times l$ with $l = 7.22$ units, we get $V_{B}=24\times7.22 = 173.28$ cubic units.

Answer:

Volume A = Volume B